[GAP Forum] Forum Digest, Vol 86, Issue 2
zahra sheikhaleslami
zahra.sheikhaleslami at gmail.com
Sun Jan 9 08:44:47 GMT 2011
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
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