[GAP Forum] Forum Digest, Vol 86, Issue 6
Sara Radfar
sararadfarss at gmail.com
Mon Jan 17 13:38:02 GMT 2011
Dear All,
Hi
Let the set of the number of sylow subgroup $G$ equal to group $PSL(2,7)$
(that is {8,21,28}) .Whether by GAP we can say $G$ is solvable group
or unsolvable group?
Thanks,
Sara
On 1/17/11, Sara Radfar <sararadfarss at gmail.com> wrote:
> Dear All,
>
> How we can by GAP conlude all automorphism group $A_7 timesA_7$?
> Thanks,
> Sara
>
> On 1/16/11, forum-request at gap-system.org <forum-request at gap-system.org>
> wrote:
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>>
>> Today's Topics:
>>
>> 1. Re: Changing memory allocation for GAP
>> (Asst. Prof. Dmitrii (Dima) Pasechnik)
>> 2. why zoo? (Igor Korepanov)
>> 3. how TzGo worked with us (Igor Korepanov)
>> 4. Re: why zoo? (Frank L?beck)
>> 5. Re: why zoo? (Asst. Prof. Dmitrii (Dima) Pasechnik)
>> 6. Re: Changing memory allocation for GAP (Frank L?beck)
>> 7. Re: how TzGo worked with us (Alexander Hulpke)
>> 8. Analogue of IsFFEMatrixGroup for matrix groups over ZmodnZ
>> (Max Horn)
>> 9. Re: Analogue of IsFFEMatrixGroup for matrix groups over
>> ZmodnZ (Alexander Hulpke)
>> 10. Creating block matrices (Katie Morrison)
>>
>>
>> ----------------------------------------------------------------------
>>
>> Message: 1
>> Date: Wed, 12 Jan 2011 18:09:05 -0800
>> From: "Asst. Prof. Dmitrii (Dima) Pasechnik" <dima at ntu.edu.sg>
>> To: Sandeep Murthy <sandeepr.murthy at gmail.com>
>> Cc: GAP forum <forum at gap-system.org>
>> Subject: Re: [GAP Forum] Changing memory allocation for GAP
>> Message-ID:
>> <AANLkTi=jRoG-pKmdrSjSkskLXBUPE4a6oPYbnE=bcDCs at mail.gmail.com>
>> Content-Type: text/plain; charset="UTF-8"
>>
>> Dear Sandeep,
>> it looks as if you start GAP in a wrong way.
>> (cause these > Error, file "-L" must exist and be readable
>>> Error, file "-m" must exist and be readable
>>> Error, file "128m" must exist and be readable
>>> Error, file "-o" must exist and be readable
>>> Error, file "512m" must exist and be readable
>> things are mangled details of command line arguments...)
>>
>> One way that works is to start it in a Terminal window.
>> Another is to use a special MacOSX application.
>>
>> Hope this helps,
>> Dmitrii
>>
>> On 12 January 2011 12:29, Sandeep Murthy <sandeepr.murthy at gmail.com>
>> wrote:
>>> Hello.
>>>
>>> Is there a command for starting GAP from the command line to
>>> open with a higher memory allocation, like 256 MB, than the standard
>>> one?
>>>
>>> I use GAP v.4.4.12 on Mac OS Leopard. At present, when I start GAP
>>> I see the following:
>>>
>>> --------
>>>
>>> Loading the library. Please be patient, this may take a while.
>>> GAP4, Version: 4.4.12 of 17-Dec-2008, i686-apple-darwin9.6.0-gcc
>>> Components: small 2.1, small2 2.0, small3 2.0, small4 1.0, small5 1.0,
>>> small6 1.0, small7 1.0, small8 1.0, small9 1.0, small10 0.2,
>>> id2 3.0, id3 2.1, id4 1.0, id5 1.0, id6 1.0, id9 1.0, id10
>>> 0.1,
>>> trans 1.0, prim 2.1 loaded.
>>> Packages: AutPGrp 1.2, CTblLib 1.1.3, TomLib 1.1.4, FactInt 1.5.2,
>>> GAPDoc 1.2 loaded.
>>> Error, file "-L" must exist and be readable
>>> Error, file "-m" must exist and be readable
>>> Error, file "128m" must exist and be readable
>>> Error, file "-o" must exist and be readable
>>> Error, file "512m" must exist and be readable
>>>
>>> --------
>>>
>>> I run search algorithms on groups of exponential complexity, and they
>>> are intrinsically slow. But I'm hoping that by using a higher initial
>>> memory allocation, for practical purposes, my programs will cover
>>> more of the search space than they have so far.
>>>
>>> Sincerely, Sandeep.
>>>
>>>
>>> _______________________________________________
>>> Forum mailing list
>>> Forum at mail.gap-system.org
>>> http://mail.gap-system.org/mailman/listinfo/forum
>>>
>>
>>
>>
>> --
>> Dmitrii Pasechnik
>> -----
>> DISCLAIMER: Any text following this sentence does not constitute a
>> part of this message, and was added automatically during transmission.
>>
>> 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: 2
>> Date: Thu, 13 Jan 2011 10:54:22 +0300
>> From: Igor Korepanov <paloff at ya.ru>
>> To: forum at gap-system.org
>> Subject: [GAP Forum] why zoo?
>> Message-ID: <491691294905262 at web47.yandex.ru>
>> Content-Type: text/plain
>>
>> Just one more question: is .zoo a somehow preferred way of archiving for
>> GAP
>> people? And why so if .tar.bz2 is so evidently better?
>>
>> Igor
>>
>>
>>
>> ------------------------------
>>
>> Message: 3
>> Date: Thu, 13 Jan 2011 11:22:21 +0300
>> From: Igor Korepanov <paloff at ya.ru>
>> To: forum at gap-system.org
>> Subject: [GAP Forum] how TzGo worked with us
>> Message-ID: <191761294906941 at web4.yandex.ru>
>> Content-Type: text/plain
>>
>> And still one more comment: we calculated yesterday the fundamental group
>> of
>> the 4-dimensional torus, which is, as everybody knows, the *abelian*
>> group
>> with 4 generators. That is, the Fp Group with 4 generators and 6 relation
>> of
>> type a * b * a^-1 * b^-1 .
>>
>> And all that was happily present in our GAP result, but besides that,
>> there
>> was one more redundant relation which we could derive manually from 6
>> others, but the TzGo algorithm apparently could not!
>>
>> We used some stuff of our own to define this fundamental group and then
>> the
>> usual TzGo command to simplify it.
>>
>> Of course I've heard of undecidable problems and stuff (as I am currently
>> employed as a university lecturer, like many people on this forum). But
>> this
>> particular problem must be decidable (here I searched Internet for a
>> suitable English interjection like "er?" to end my letter, but found only
>> some strange "Ekh-ma" http://en.wikipedia.org/wiki/Ekh_%28expression%29 )
>> ?
>>
>> Best wishes,
>>
>> Igor
>>
>>
>>
>> ------------------------------
>>
>> Message: 4
>> Date: Thu, 13 Jan 2011 10:37:54 +0100
>> From: Frank L?beck <frank.luebeck at math.rwth-aachen.de>
>> To: forum at gap-system.org
>> Subject: Re: [GAP Forum] why zoo?
>> Message-ID: <20110113093754.GA19326 at beteigeuze>
>> Content-Type: text/plain; charset=iso-8859-1
>>
>> On Thu, Jan 13, 2011 at 10:54:22AM +0300, Igor Korepanov wrote:
>>> Just one more question: is .zoo a somehow preferred way of archiving for
>>> GAP people? And why so if .tar.bz2 is so evidently better?
>>
>> But all of our archives are provided in .zoo, .tar.gz, .tar.bz2 and
>> -win.zip
>> format. You are free to use what you like most!
>>
>> .tar.bz2 is not "evidently better", e.g. it does not unpack text files
>> under Windows/DOS with the native line break convention, and it is much
>> slower to unpack them compared to, say, .tar.gz.
>>
>> See
>> http://www.gap-system.org/Download/formats.html
>> for more details.
>>
>> Best regards,
>> Frank L?beck
>>
>> --
>> /// Dr. Frank L?beck, Lehrstuhl D f?r Mathematik, Templergraben 64, ///
>> \\\ 52062 Aachen, Germany \\\
>> /// E-mail: Frank.Luebeck at Math.RWTH-Aachen.De ///
>> \\\ WWW: http://www.math.rwth-aachen.de/~Frank.Luebeck/ \\\
>>
>>
>>
>>
>> ------------------------------
>>
>> Message: 5
>> Date: Thu, 13 Jan 2011 01:58:45 -0800
>> From: "Asst. Prof. Dmitrii (Dima) Pasechnik" <dima at ntu.edu.sg>
>> To: Igor Korepanov <paloff at ya.ru>
>> Cc: "forum at gap-system.org" <forum at gap-system.org>
>> Subject: Re: [GAP Forum] why zoo?
>> Message-ID:
>> <AANLkTik6umPeM+FwevF26x+bwatfWBOyvW=FZPpSyc-Q at mail.gmail.com>
>> Content-Type: text/plain; charset="UTF-8"
>>
>> Igor,
>> .zoo is an old format, historically the first GAP was using, exclusively.
>>
>> About 10 years ago there were long discussions on this list whether one
>> should use other formats, and common sense prevailed, so .zoo is no
>> longer
>> the only format used.
>> Perhaps .zoo will be retired at some point...
>>
>> On 12 January 2011 23:54, Igor Korepanov <paloff at ya.ru> wrote:
>>> Just one more question: is .zoo a somehow preferred way of archiving for
>>> GAP people? And why so if .tar.bz2 is so evidently better?
>>>
>>> Igor
>>>
>>> _______________________________________________
>>> Forum mailing list
>>> Forum at mail.gap-system.org
>>> http://mail.gap-system.org/mailman/listinfo/forum
>>>
>>
>>
>>
>> --
>> Dmitrii Pasechnik
>> -----
>> DISCLAIMER: Any text following this sentence does not constitute a
>> part of this message, and was added automatically during transmission.
>>
>> 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: 6
>> Date: Thu, 13 Jan 2011 17:41:18 +0100
>> From: Frank L?beck <frank.luebeck at math.rwth-aachen.de>
>> To: Sandeep Murthy <sandeepr.murthy at gmail.com>, forum at gap-system.org
>> Subject: Re: [GAP Forum] Changing memory allocation for GAP
>> Message-ID: <20110113164117.GB26842 at beteigeuze>
>> Content-Type: text/plain; charset=iso-8859-1
>>
>> On Wed, Jan 12, 2011 at 08:29:24PM +0000, Sandeep Murthy wrote:
>>> Is there a command for starting GAP from the command line to
>>> open with a higher memory allocation, like 256 MB, than the standard
>>> one?
>>>
>>> I use GAP v.4.4.12 on Mac OS Leopard. At present, when I start GAP
>>> I see the following:
>>>
>>> --------
>>>
>>> Loading the library. Please be patient, this may take a while.
>>> GAP4, Version: 4.4.12 of 17-Dec-2008, i686-apple-darwin9.6.0-gcc
>>> Components: small 2.1, small2 2.0, small3 2.0, small4 1.0, small5 1.0,
>>> small6 1.0, small7 1.0, small8 1.0, small9 1.0, small10
>>> 0.2,
>>> id2 3.0, id3 2.1, id4 1.0, id5 1.0, id6 1.0, id9 1.0, id10
>>> 0.1,
>>> trans 1.0, prim 2.1 loaded.
>>> Packages: AutPGrp 1.2, CTblLib 1.1.3, TomLib 1.1.4, FactInt 1.5.2,
>>> GAPDoc 1.2 loaded.
>>> Error, file "-L" must exist and be readable
>>> Error, file "-m" must exist and be readable
>>> Error, file "128m" must exist and be readable
>>> Error, file "-o" must exist and be readable
>>> Error, file "512m" must exist and be readable
>>>
>>
>>
>> Dear Sandeep Murphy, dear Forum,
>>
>> To find an explaination in the GAP documentation type
>>
>> ?command line options
>>
>> into your GAP session. If one of the arguments in your call of GAP is
>> a file name, then all further arguments are also interpreted as file
>> names.
>>
>> So you should call GAP like:
>> gap -m 128m -o 512m [maybe more options here] file1 file2 ...
>>
>> Using the -m option with a larger amount of memory does usually not give
>> a big performance advantage. But using a higher value with the -o option
>> causes that you see a message of form
>>
>> exceeded the permitted memory (`-o' command line option) at
>> [...]
>> brk>
>>
>> later than with the default value. (You can type 'return;' at that
>> brk-prompt, then GAP doubles the value of the -o option.)
>> Nevertheless, it does not make sense to specify with -o more memory than
>> your GAP job has available as physical memory.
>>
>> With best regards,
>> Frank L?beck
>>
>> --
>> /// Dr. Frank L?beck, Lehrstuhl D f?r Mathematik, Templergraben 64, ///
>> \\\ 52062 Aachen, Germany \\\
>> /// E-mail: Frank.Luebeck at Math.RWTH-Aachen.De ///
>> \\\ WWW: http://www.math.rwth-aachen.de/~Frank.Luebeck/ \\\
>>
>>
>>
>>
>> ------------------------------
>>
>> Message: 7
>> Date: Thu, 13 Jan 2011 10:20:17 -0700
>> From: Alexander Hulpke <hulpke at math.colostate.edu>
>> To: gap forum <forum at gap-system.org>
>> Subject: Re: [GAP Forum] how TzGo worked with us
>> Message-ID: <3196FBA1-3829-4234-A59D-9BC51E350DF3 at math.colostate.edu>
>> Content-Type: text/plain; charset=us-ascii
>>
>>
>>
>> Dear Forum,
>>
>> On Jan 13, 2011, at 1/13/11 1:22, Igor Korepanov wrote:
>>
>>> And still one more comment: we calculated yesterday the fundamental
>>> group
>>> of the 4-dimensional torus, which is, as everybody knows, the *abelian*
>>> group with 4 generators. That is, the Fp Group with 4 generators and 6
>>> relation of type a * b * a^-1 * b^-1 .
>>>
>>> And all that was happily present in our GAP result, but besides that,
>>> there was one more redundant relation which we could derive manually
>>> from
>>> 6 others, but the TzGo algorithm apparently could not!
>>
>> TzGo (the Tietze transformations command) uses a couple of heuristics,
>> based
>> on length criteria, to shorten a presentation, in particular if it was
>> obtained from rewriting to a subgroup. It does not aim to do a systematic
>> search for all redundancies. The primary aim is to get a presentation
>> shorter with a moderate amount of effort, not to get an irredundant
>> presentation or cover the largest possible class of decidable problems.
>> It
>> is clearly not optimal, but adding further attempts might cause an
>> overall
>> slowdown in other situations.
>>
>> Thus I'm not surprised that thinking (or even other algorithms that would
>> be
>> willing to devote more time) can produce better results in particular
>> situations.
>>
>> Best wishes,
>>
>> Alexander Hulpke
>>
>>
>>
>>
>> -- Colorado State University, Department of Mathematics,
>> Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
>> email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
>> http://www.math.colostate.edu/~hulpke
>>
>>
>>
>>
>>
>>
>> ------------------------------
>>
>> Message: 8
>> Date: Fri, 14 Jan 2011 15:24:16 +0100
>> From: Max Horn <max at quendi.de>
>> To: GAP Forum <Forum at gap-system.org>
>> Subject: [GAP Forum] Analogue of IsFFEMatrixGroup for matrix groups
>> over ZmodnZ
>> Message-ID: <01D99A4D-2E0A-46D6-BCA3-8B8D4163A180 at quendi.de>
>> Content-Type: text/plain; charset=us-ascii
>>
>> Dear GAP forum
>>
>> is there an analogue for IsFFEMatrixGroup and FieldOfMatrixGroup for
>> groups
>> over ZmodnZ ? Something like IsZmodnZMatrixGroup and RingOfMatrixGroup ?
>> I
>> didn't find anything like that. If it doesn't exist, how would I best go
>> about adding those?
>>
>> Background: I'd like to install my own methods for e.g. NiceMonomorphism
>> for
>> matrix groups over ZmodnZ. To illustrate why: for GL(3, Z/36Z), GAP
>> currently finds a perm rep on 39312 points, my code finds one on 758
>> points
>> (it doesn't do anything fancy or new, mind you)
>>
>> For now, I just "manually" use SetNiceMonomorphism on my groups, but I
>> thought it would be kinda nice to properly hook this into GAP (so that
>> maybe
>> it could even be integrated in a package or GAP itself one day).
>>
>>
>> Cheers,
>> Max
>>
>>
>>
>>
>> ------------------------------
>>
>> Message: 9
>> Date: Fri, 14 Jan 2011 10:03:32 -0700
>> From: Alexander Hulpke <hulpke at math.colostate.edu>
>> To: Max Horn <max at quendi.de>
>> Cc: GAP Forum <Forum at gap-system.org>
>> Subject: Re: [GAP Forum] Analogue of IsFFEMatrixGroup for matrix
>> groups over ZmodnZ
>> Message-ID: <965B2533-1AC7-486E-ACAA-32BD16BCFC42 at math.colostate.edu>
>> Content-Type: text/plain; charset=us-ascii
>>
>>
>>
>> Dear Forum,
>>
>> On Jan 14, 2011, at 1/14/11 7:24, Max Horn wrote:
>>
>>> is there an analogue for IsFFEMatrixGroup and FieldOfMatrixGroup for
>>> groups over ZmodnZ ? Something like IsZmodnZMatrixGroup and
>>> RingOfMatrixGroup ? I didn't find anything like that. If it doesn't
>>> exist,
>>> how would I best go about adding those?
>>
>> Assuming you want to catch the case for nonprime n, the equivalent for
>> IsFFEMatrixGroup would be
>> IsZmodnZObjNonprimeCollCollColl and IsMatrixGroup
>>
>> To get the underlying ring, you could use
>> DefaultRing(Flat(GeneratorsOfGroup(g)));
>>
>> Best wishes,
>>
>> Alexander Hulpke
>>
>>
>>
>>
>>
>>
>>
>> ------------------------------
>>
>> Message: 10
>> Date: Sun, 16 Jan 2011 22:21:10 -0600
>> From: Katie Morrison <kmorris2 at gmail.com>
>> To: forum at gap-system.org
>> Subject: [GAP Forum] Creating block matrices
>> Message-ID:
>> <AANLkTikx8fOUPG=ob1FxdQCpXikqYnk=-baCpcSLJnvk at mail.gmail.com>
>> Content-Type: text/plain; charset=ISO-8859-1
>>
>> Hi all, I was wondering if there's an efficient way to create the
>> subgroup
>> of GL(2n, q) consisting of block matrices of the form:
>> [A 0
>> B C]
>> where A and C are in GL(n,q) and B is in M(n,q) (i.e. B is an arbitrary
>> nxn
>> matrix). Thanks for the help.
>>
>> Katie
>>
>>
>> ------------------------------
>>
>> _______________________________________________
>> Forum mailing list
>> Forum at mail.gap-system.org
>> http://mail.gap-system.org/mailman/listinfo/forum
>>
>>
>> End of Forum Digest, Vol 86, Issue 6
>> ************************************
>>
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