[GAP Forum] Forum Digest, Vol 86, Issue 2
zahra sheikhaleslami
zahra.sheikhaleslami at gmail.com
Sun Jan 9 08:50:47 GMT 2011
let H1,H2
be characteristic subgroupsof a given group
G=H1×H2
ٰthen
K(H1×H2)=K(H1)×K(H2)
please give with gap
i need
On 1/9/11, zahra sheikhaleslami <zahra.sheikhaleslami at gmail.com> wrote:
> hi
> please write this theorem with gap
>
> if G,H are finite groups with (IGI,IHI)=1then
> Aut(G×H)=Aut(G)×Aut(H)
>
> On 1/9/11, forum-request at gap-system.org <forum-request at gap-system.org>
> wrote:
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>> Today's Topics:
>>
>> 1. Help (Sara Radfar)
>> 2. Re: Help (Vipul Naik)
>> 3. Re: Help (Dr. Ashish Kumar Das)
>> 4. First Announcement:Workshop on "Finite Groups & Their
>> Automorphisms" in Istanbul (Gulin Ercan)
>> 5. Re: Interface with other languages (Alexander Konovalov)
>> 6. The Add function (Hebert P?rez-Ros?s)
>> 7. Re: The Add function (Keshav Rao Kini)
>> 8. Re: The Add function (Hebert P?rez-Ros?s)
>> 9. Question (Sara Radfar)
>>
>>
>> ----------------------------------------------------------------------
>>
>> Message: 1
>> Date: Thu, 6 Jan 2011 05:14:32 -0800
>> From: Sara Radfar <sararadfarss at gmail.com>
>> To: forum <forum at gap-system.org>
>> Subject: [GAP Forum] Help
>> Message-ID:
>> <AANLkTikj7bGYABa0KaUiu_VXOc9jAo2s3KuMRR_Xbxcz at mail.gmail.com>
>> Content-Type: text/plain; charset=ISO-8859-1
>>
>> Hi
>>
>> I can find the same order elements of a group but can't find the set
>> of the number of the same order elements of a group.Also how we can
>> introduce a sporadic simple group to GAP?.For example $CO$.
>>
>> Thanks
>> Sara
>>
>>
>>
>> ------------------------------
>>
>> Message: 2
>> Date: Thu, 6 Jan 2011 20:22:04 -0600
>> From: Vipul Naik <vipul at math.uchicago.edu>
>> To: Sara Radfar <sararadfarss at gmail.com>
>> Cc: forum <forum at gap-system.org>
>> Subject: Re: [GAP Forum] Help
>> Message-ID: <20110107022204.GA16678 at math.uchicago.edu>
>> Content-Type: text/plain; charset=us-ascii
>>
>> Hi,
>>
>> If I understand your question correctly, you want information on how
>> many elements of a finite group have each possible order. Although I
>> don't think there are built-in functions for this, it is easy to write
>> code for these. For instance:
>>
>> OrderStatisticsPaired := function(G)
>> local L,D;
>> L := List(Set(G),Order);
>> D := DivisorsInt(Order(G));
>> return(List(D,x->[x,Length(Filtered(L,y->x=y))]));
>> end;;
>>
>> This function takes as input a group and gives a list of ordered
>> pairs, for each divisor of the order of the group, how many elements
>> of the group have that order. For instance:
>>
>> OrderStatisticsPaired(SymmetricGroup(4))
>>
>> gives the output:
>>
>> [ [ 1, 1 ], [ 2, 9 ], [ 3, 8 ], [ 4, 6 ], [ 6, 0 ], [ 8, 0 ], [ 12, 0 ],
>> [
>> 24, 0 ] ]
>>
>> indicating that in the symmetric group on four letters, there is one
>> element of the group of order one, nine elements of order two, eight
>> elements of order three, six elements of order four, and no element of
>> any higher order.
>>
>> This exact function may not suit your needs but it's likely that some
>> variant of it will.
>>
>> This code is inefficient for large groups; for such groups, one can
>> modify the code to only go over conjugacy classes instead of elements.
>>
>> To create such a function, you can either paste the function code in
>> front of the GAP command prompt or include this in a file and then use
>> GAP's "Read" command to read that file in.
>>
>> Vipul
>>
>> * Quoting Sara Radfar who at 2011-01-06 05:14:32+0000 (Thu) wrote
>>> Hi
>>>
>>> I can find the same order elements of a group but can't find the set
>>> of the number of the same order elements of a group.Also how we can
>>> introduce a sporadic simple group to GAP?.For example $CO$.
>>>
>>> Thanks
>>> Sara
>>>
>>> _______________________________________________
>>> Forum mailing list
>>> Forum at mail.gap-system.org
>>> http://mail.gap-system.org/mailman/listinfo/forum
>>
>>
>>
>> ------------------------------
>>
>> Message: 3
>> Date: Fri, 7 Jan 2011 10:02:53 +0530
>> From: "Dr. Ashish Kumar Das" <akdasnehu at gmail.com>
>> To: Vipul Naik <vipul at math.uchicago.edu>
>> Cc: Sara Radfar <sararadfarss at gmail.com>, forum <forum at gap-system.org>
>> Subject: Re: [GAP Forum] Help
>> Message-ID:
>> <AANLkTim7KGWxE11Z7QDGyMTWpOxJs9YifonuW1RmwzpR at mail.gmail.com>
>> Content-Type: text/plain; charset=ISO-8859-1
>>
>> Hi,
>> How about running the following program:
>>
>>
>> n:=90; # try with other values
>> i:=0;
>> Print("GROUP ORDER is ", " ", n, "\n");
>> g:= AllSmallGroups(n);
>> for xx in g do
>> i:=i+1;
>> Print( "\n", "SMALL GROUP", "(" , n, "," , i, ") =
>> ",StructureDescription(xx), "\n","\n");
>> yy:= Set(List(xx,Order));
>> for y in yy do
>> zz:= Number(xx, x -> Order(x)=y);
>> Print("order = ", y, " ", "number of elts = ", zz, "\n", "\n"); od;
>> od;
>>
>> Ashish Kumar Das
>> Maths Dept.
>> NEHU, Shillong, INDIA
>>
>> On 1/7/11, Vipul Naik <vipul at math.uchicago.edu> wrote:
>>> Hi,
>>>
>>> If I understand your question correctly, you want information on how
>>> many elements of a finite group have each possible order. Although I
>>> don't think there are built-in functions for this, it is easy to write
>>> code for these. For instance:
>>>
>>> OrderStatisticsPaired := function(G)
>>> local L,D;
>>> L := List(Set(G),Order);
>>> D := DivisorsInt(Order(G));
>>> return(List(D,x->[x,Length(Filtered(L,y->x=y))]));
>>> end;;
>>>
>>> This function takes as input a group and gives a list of ordered
>>> pairs, for each divisor of the order of the group, how many elements
>>> of the group have that order. For instance:
>>>
>>> OrderStatisticsPaired(SymmetricGroup(4))
>>>
>>> gives the output:
>>>
>>> [ [ 1, 1 ], [ 2, 9 ], [ 3, 8 ], [ 4, 6 ], [ 6, 0 ], [ 8, 0 ], [ 12, 0 ],
>>> [
>>> 24, 0 ] ]
>>>
>>> indicating that in the symmetric group on four letters, there is one
>>> element of the group of order one, nine elements of order two, eight
>>> elements of order three, six elements of order four, and no element of
>>> any higher order.
>>>
>>> This exact function may not suit your needs but it's likely that some
>>> variant of it will.
>>>
>>> This code is inefficient for large groups; for such groups, one can
>>> modify the code to only go over conjugacy classes instead of elements.
>>>
>>> To create such a function, you can either paste the function code in
>>> front of the GAP command prompt or include this in a file and then use
>>> GAP's "Read" command to read that file in.
>>>
>>> Vipul
>>>
>>> * Quoting Sara Radfar who at 2011-01-06 05:14:32+0000 (Thu) wrote
>>>> Hi
>>>>
>>>> I can find the same order elements of a group but can't find the set
>>>> of the number of the same order elements of a group.Also how we can
>>>> introduce a sporadic simple group to GAP?.For example $CO$.
>>>>
>>>> Thanks
>>>> Sara
>>>>
>>>> _______________________________________________
>>>> Forum mailing list
>>>> Forum at mail.gap-system.org
>>>> http://mail.gap-system.org/mailman/listinfo/forum
>>>
>>> _______________________________________________
>>> Forum mailing list
>>> Forum at mail.gap-system.org
>>> http://mail.gap-system.org/mailman/listinfo/forum
>>>
>>
>>
>>
>> ------------------------------
>>
>> Message: 4
>> Date: Fri, 07 Jan 2011 11:25:42 +0200
>> From: Gulin Ercan <ercan at metu.edu.tr>
>> To: forum at gap-system.org
>> Subject: [GAP Forum] First Announcement:Workshop on "Finite Groups &
>> Their Automorphisms" in Istanbul
>> Message-ID: <20110107112542.104653muq7sbzqja at horde.metu.edu.tr>
>> Content-Type: text/plain; charset=ISO-8859-9; DelSp="Yes";
>> format="flowed"
>>
>> Dear All,
>>
>> We would like to announce herewith a five-day workshop on "Finite
>> groups and their automorphisms"
>> which will take place in Istanbul at Bo?azi?i University on 7-11 June
>> 2011.
>>
>> It aims to bring together leading mathematicians and active
>> researchers working on
>> the theory of groups in order to exchange ideas, present new results and
>> identify the key problems in the field.
>>
>> The workshop is especially interested in and motivated by the
>> questions on the relationship
>> between a finite group and another one acted upon by the first,
>> although it is not to be considered the exclusive theme.
>>
>> There will be seven mini-courses and some invited talks.
>> The speakers who have kindly accepted our invitation to give (a short
>> series of)lectures are:
>>
>> Alan Camina, Martin I.Isaacs, Evgeny Khukhro, Charles Leedham-Green,
>> Attila Maroti, Nadia Mazza, Akos Seress, Aner Shalev and Said N.Sidki
>>
>> There will be a limited number of slots available in the schedule for
>> contributed talks as well
>> and a poster session.
>>
>> For details and registration please visit the workshop webpage
>> http://www.istanbulgroup.metu.edu.tr
>>
>> We are looking forward to seeing you in Istanbul!!
>>
>>
>>
>>
>>
>>
>> ----------------------------------------------------------------
>> This message was sent using IMP, the Internet Messaging Program.
>>
>>
>>
>>
>> ------------------------------
>>
>> Message: 5
>> Date: Fri, 7 Jan 2011 15:58:05 +0000
>> From: Alexander Konovalov <alexander.konovalov at gmail.com>
>> To: bart at mat.ug.edu.pl
>> Cc: forum at gap-system.org
>> Subject: Re: [GAP Forum] Interface with other languages
>> Message-ID: <1D984673-C91C-4F6B-B493-D1843C9E5090 at gmail.com>
>> Content-Type: text/plain; charset=us-ascii
>>
>> Dear Bartosz, dear GAP Forum,
>>
>> There are already several GAP packages that contain C parts and
>> use LoadDynamicModule to load them, so probably to begin with
>> you may have a look at them. In no particular order, these packages
>> are: orb, linboxing, io, HAP, Gauss, FR, EDIM and Browse.
>>
>> Best wishes,
>> Alexander
>>
>>
>> On 10 Dec 2010, at 14:44, bart at mat.ug.edu.pl wrote:
>>
>>> W dniu 10.12.2010 10:06, Max Horn pisze:
>>>> In addition, GAP can load dynamic modules (again, at least on UNIX type
>>> systems). I used that to implement some of the most time critical
>>> functions of a package I am working on in C, for a major speed boost.
>>> So
>>> you could call other systems from within GAP
>>>
>>> Hello,
>>>
>>> How to do this?
>>> Could I write my own function in C/C++, compile it into library, and use
>>> in GAP?
>>> I imagine that there could be necessary some types conversions (?)
>>>
>>> I see LoadDynamicModule() in
>>> http://www.gap-system.org/Manuals/doc/htm/ref/CHAP003.htm#SECT007
>>> but is it possible to use it with library other than obtained by using
>>> gac?
>>>
>>>
>>> All the best
>>> Bartosz Putrycz
>>
>>
>>
>> ------------------------------
>>
>> Message: 6
>> Date: Sat, 8 Jan 2011 16:31:23 +1100
>> From: Hebert P?rez-Ros?s <hebert.perez at gmail.com>
>> To: forum at gap-system.org
>> Subject: [GAP Forum] The Add function
>> Message-ID:
>> <AANLkTimSVW54Q2VbLEwjv-BMECvOM+d=3W3H5Ex3MYLA at mail.gmail.com>
>> Content-Type: text/plain; charset=ISO-8859-1
>>
>> Dear all,
>>
>> I'm embarrased to say this, but I'm very puzzled by the behaviour of the
>> Add
>> function. I have this simple test code:
>>
>> --------------------------------------
>> TestFun:= function(n)
>> local perm, out, i;
>>
>> out:= [];
>> perm:= [];
>> for i in [1..n] do
>> perm[i]:=0;
>> od;
>> for i in [1..n] do
>> perm[i]:= i;
>> Add(out, perm);
>> od;
>> return out;
>> end;
>> ----------------------------------
>>
>> If I now make a call to Test(3), I should get [ [1,0,0], [1,2,0], [1,2,3]
>> ],
>> right? However, I'm getting [ [1,2,3], [1,2,3], [1,2,3] ]. Do you get the
>> same thing? Can anybody explain to me what's happening here?
>>
>> Thank you very much in advance,
>>
>> Hebert Perez-Roses
>> The University of Newcastle, Australia
>>
>>
>> ------------------------------
>>
>> Message: 7
>> Date: Sat, 8 Jan 2011 14:01:44 +0800
>> From: Keshav Rao Kini <krkini at ntu.edu.sg>
>> To: Hebert P?rez-Ros?s <hebert.perez at gmail.com>
>> Cc: "forum at gap-system.org" <forum at gap-system.org>
>> Subject: Re: [GAP Forum] The Add function
>> Message-ID:
>> <AANLkTinqc2AoEPyeeeYx8nXezmgDm1YxtBQrK0+r=Bxx at mail.gmail.com>
>> Content-Type: text/plain; charset="utf-8"
>>
>> Hello,
>>
>> Each time you use Add, it adds perm as a new list entry in out. It does
>> NOT
>> add the current value of perm as a new list entry in out, but rather
>> inserts
>> a reference to the list perm. The list perm is added to the list out
>> three
>> times, and by the time the function returns, perm = [1,2,3], so out
>> consists
>> of three [1,2,3].
>>
>> If you want to remember previous states of a list, you'll always need to
>> make a copy, because this is not done automatically when using functions
>> like Add. Try using for example the ShallowCopy function.
>>
>> Hope that helps.
>>
>> Yours,
>> Keshav
>>
>> Disclaimer: the boilerplate text at the foot of this email has been added
>> automatically by my mail server. This was not done by my request (rather
>> the
>> opposite) so please disregard it.
>>
>>
>>
>> 2011/1/8 Hebert P?rez-Ros?s
>> <hebert.perez at gmail.com<mailto:hebert.perez at gmail.com>>
>> Dear all,
>>
>> I'm embarrased to say this, but I'm very puzzled by the behaviour of the
>> Add
>> function. I have this simple test code:
>>
>> --------------------------------------
>> TestFun:= function(n)
>> local perm, out, i;
>>
>> out:= [];
>> perm:= [];
>> for i in [1..n] do
>> perm[i]:=0;
>> od;
>> for i in [1..n] do
>> perm[i]:= i;
>> Add(out, perm);
>> od;
>> return out;
>> end;
>> ----------------------------------
>>
>> If I now make a call to Test(3), I should get [ [1,0,0], [1,2,0], [1,2,3]
>> ],
>> right? However, I'm getting [ [1,2,3], [1,2,3], [1,2,3] ]. Do you get the
>> same thing? Can anybody explain to me what's happening here?
>>
>> Thank you very much in advance,
>>
>> Hebert Perez-Roses
>> The University of Newcastle, Australia
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org<mailto:Forum at mail.gap-system.org>
>> http://mail.gap-system.org/mailman/listinfo/forum
>>
>>
>> ________________________________
>> CONFIDENTIALITY: This email is intended solely for the person(s) named
>> and
>> may be confidential and/or privileged. If you are not the intended
>> recipient, please delete it, notify us and do not copy, use, or disclose
>> its
>> content. Thank you.
>>
>> Towards A Sustainable Earth: Print Only When Necessary
>>
>>
>> ------------------------------
>>
>> Message: 8
>> Date: Sat, 8 Jan 2011 17:19:17 +1100
>> From: Hebert P?rez-Ros?s <hebert.perez at gmail.com>
>> To: Keshav Rao Kini <krkini at ntu.edu.sg>
>> Cc: "forum at gap-system.org" <forum at gap-system.org>
>> Subject: Re: [GAP Forum] The Add function
>> Message-ID:
>> <AANLkTi=45xTJpXaSw-97paYrHFKOvTvcDqd_8Og4sZoJ at mail.gmail.com>
>> Content-Type: text/plain; charset=ISO-8859-1
>>
>> OK, thank you very much. I would just swear that I had already tried
>> that.
>> Cheers,
>> Hebert.
>>
>>
>> 2011/1/8 Keshav Rao Kini <krkini at ntu.edu.sg>
>>
>>> Hello,
>>>
>>> Each time you use Add, it adds perm as a new list entry in out. It does
>>> NOT
>>> add the current value of perm as a new list entry in out, but rather
>>> inserts
>>> a reference to the list perm. The list perm is added to the list out
>>> three
>>> times, and by the time the function returns, perm = [1,2,3], so out
>>> consists
>>> of three [1,2,3].
>>>
>>> If you want to remember previous states of a list, you'll always need to
>>> make a copy, because this is not done automatically when using functions
>>> like Add. Try using for example the ShallowCopy function.
>>>
>>> Hope that helps.
>>>
>>> Yours,
>>> Keshav
>>>
>>> Disclaimer: the boilerplate text at the foot of this email has been
>>> added
>>> automatically by my mail server. This was not done by my request (rather
>>> the
>>> opposite) so please disregard it.
>>>
>>>
>>>
>>> 2011/1/8 Hebert P?rez-Ros?s <hebert.perez at gmail.com>
>>>
>>>> Dear all,
>>>>
>>>> I'm embarrased to say this, but I'm very puzzled by the behaviour of
>>>> the
>>>> Add
>>>> function. I have this simple test code:
>>>>
>>>> --------------------------------------
>>>> TestFun:= function(n)
>>>> local perm, out, i;
>>>>
>>>> out:= [];
>>>> perm:= [];
>>>> for i in [1..n] do
>>>> perm[i]:=0;
>>>> od;
>>>> for i in [1..n] do
>>>> perm[i]:= i;
>>>> Add(out, perm);
>>>> od;
>>>> return out;
>>>> end;
>>>> ----------------------------------
>>>>
>>>> If I now make a call to Test(3), I should get [ [1,0,0], [1,2,0],
>>>> [1,2,3]
>>>> ],
>>>> right? However, I'm getting [ [1,2,3], [1,2,3], [1,2,3] ]. Do you get
>>>> the
>>>> same thing? Can anybody explain to me what's happening here?
>>>>
>>>> Thank you very much in advance,
>>>>
>>>> Hebert Perez-Roses
>>>> The University of Newcastle, Australia
>>>> _______________________________________________
>>>> Forum mailing list
>>>> Forum at mail.gap-system.org
>>>> http://mail.gap-system.org/mailman/listinfo/forum
>>>>
>>>
>>>
>>> ------------------------------
>>> CONFIDENTIALITY: This email is intended solely for the person(s) named
>>> and
>>> may be confidential and/or privileged. If you are not the intended
>>> recipient, please delete it, notify us and do not copy, use, or disclose
>>> its
>>> content. Thank you.
>>>
>>> Towards A Sustainable Earth: Print Only When Necessary
>>>
>>
>>
>> ------------------------------
>>
>> Message: 9
>> Date: Sun, 9 Jan 2011 00:32:23 -0800
>> From: Sara Radfar <sararadfarss at gmail.com>
>> To: forum at gap-system.org
>> Subject: [GAP Forum] Question
>> Message-ID:
>> <AANLkTin5mrpG3+N3f85+Dbco_NB=L_9JHJ7yFJLwvCsK at mail.gmail.com>
>> Content-Type: text/plain; charset=ISO-8859-1
>>
>> Dear forum
>> Hi
>> I have a question about group theory.I know that should send this
>> message for group pub forum but I coudn't join to it.If you can help
>> me about my question:
>> My question is:Let the set of the number of sylow subgroup $G$ equal
>> to group $PSL(2,7)$(that is {8,21,28}) about solvability or
>> unsolvability group $G$ what we can say?
>> Thanks
>> sara
>>
>>
>>
>> ------------------------------
>>
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum
>>
>>
>> End of Forum Digest, Vol 86, Issue 2
>> ************************************
>>
>
>
> --
> zahra sheikhaleslami
>
--
zahra sheikhaleslami
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