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Update website for ModIsom 3.0.0
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fingolfin committed Sep 21, 2024
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67 changes: 58 additions & 9 deletions PackageInfo.g
Original file line number Diff line number Diff line change
@@ -1,16 +1,16 @@
#############################################################################
##
##
## PackageInfo.g for the package `modisom' Bettina Eick
##
##
SetPackageInfo( rec(
PackageName := "ModIsom",
Subtitle := "Computing automorphisms and checking isomorphisms for modular group algebras of finite p-groups",
Version := "2.5.4",
Date := "27/02/2023", # dd/mm/yyyy format
Version := "3.0.0",
Date := "20/09/2024", # dd/mm/yyyy format
License := "GPL-2.0-or-later",

Persons := [
rec(
rec(
LastName := "Eick",
FirstNames := "Bettina",
IsAuthor := true,
Expand All @@ -26,6 +26,23 @@ Persons := [
Place := "Braunschweig",
Institution := "TU Braunschweig"
),

rec(
LastName := "Garcia-Lucas",
FirstNames := "Diego",
IsAuthor := true,
IsMaintainer := false,
Email := "[email protected]",
PostalAddress := Concatenation(
"Departamento de Matematicas\n",
"Facultad de Matematicas\n",
"Universidad de Murcia\n",
"ES-30100 Murcia\n",
"Spain" ),
Place := "Murcia",
Institution := "Universidad de Murcia"
),

rec(
LastName := "Konovalov",
FirstNames := "Olexandr",
Expand All @@ -40,7 +57,39 @@ Persons := [
"St Andrews, Fife, KY16 9SX, Scotland" ] ),
Place := "St Andrews",
Institution := "University of St Andrews"
) ],
),
rec(
LastName := "Margolis",
FirstNames := "Leo",
IsAuthor := true,
IsMaintainer := true,
Email := "[email protected]",
WWWHome := "http://www.margollo.github.io",
PostalAddress := Concatenation(
"Departamento de Matematicas\n",
"Universidad Autonoma de Madrid\n",
"Campus Cantoblanco\n",
"28049 Madrid\n",
"Spain" ),
Place := "Madrid",
Institution := "Universidad Autonoma de Madrid"
),
rec(
LastName := "Moede",
FirstNames := "Tobias",
IsAuthor := true,
IsMaintainer := false,
Email := "[email protected]",
WWWHome := "https://www.tu-braunschweig.de/iaa/personal/moede",
PostalAddress := Concatenation( [
"Institute of Analysis and Algebra\n",
"TU Braunschweig\n",
"Universitaetsplatz 2, 38106 Braunschweig\n",
"Germany" ] ),
Place := "Braunschweig",
Institution := "TU Braunschweig"
)
],

Status := "accepted",
CommunicatedBy := "Olexandr Konovalov (St Andrews)",
Expand All @@ -59,7 +108,7 @@ ArchiveURL := Concatenation( ~.SourceRepository.URL,
"/modisom-", ~.Version ),
ArchiveFormats := ".tar.gz",

AbstractHTML :=
AbstractHTML :=
"The <span class=\"pkgname\">ModIsom</span> package contains various methods for computing with nilpotent associative algebras. In particular, it contains a method to determine the automorphism group and to test isomorphis of such algebras over finite fields and of modular group algebras of finite p-groups, and it contains a nilpotent quotient algorithm for finitely presented associative algebras and a method to determine Kurosh algebras.",

PackageDoc := rec(
Expand All @@ -75,7 +124,7 @@ PackageDoc := rec(

Dependencies := rec(
GAP := ">=4.7",
NeededOtherPackages := [["Polycyclic", ">=1.0"]],
NeededOtherPackages := [["Polycyclic", ">=1.0"]],
SuggestedOtherPackages := [],
ExternalConditions := []
),
Expand All @@ -85,7 +134,7 @@ AvailabilityTest := ReturnTrue,
Autoload := false,
TestFile := "tst/testall.g",
Keywords := ["modular isomorphism problem",
"automorphism group",
"automorphism group",
"isomorphism testing",
"nilpotent algebras",
"nilpotent quotient",
Expand Down
5 changes: 5 additions & 0 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -10,6 +10,10 @@ determine the automorphism group and to test isomorphis of such algebras
over finite fields and of modular group algebras of finite p-groups, and
it contains a nilpotent quotient algorithm for finitely presented associative
algebras and a method to determine Kurosh algebras.
Some of the functions to compute with nilpotent algebras are tailored towards
application for the Modular Isomorphism Problem.
Moreover, the package allows to compute various group theoretical properties of groups
related to the Modular Isomorphism Problem.


## Installation
Expand All @@ -29,3 +33,4 @@ your installation is complete. To load the package, call

The manual of ModIsom is contained in `modisom/doc` and `modisom/htm`
directories.

39 changes: 24 additions & 15 deletions _data/package.yml
Original file line number Diff line number Diff line change
@@ -1,19 +1,27 @@
name: ModIsom
version: "2.5.4"
version: "3.0.0"
license: "GPL-2.0-or-later"
date: 2023-02-27
date: 2024-09-20
description: |
Computing automorphisms and checking isomorphisms for modular group algebras of finite p-groups
authors:
- name: Bettina Eick
url: http://www.iaa.tu-bs.de/beick
- name: Diego Garcia-Lucas
url: mailto:[email protected]
- name: Leo Margolis
url: http://www.margollo.github.io
- name: Tobias Moede
url: https://www.tu-braunschweig.de/iaa/personal/moede

maintainers:
- name: Bettina Eick
url: http://www.iaa.tu-bs.de/beick
- name: Olexandr Konovalov
url: https://olexandr-konovalov.github.io/
- name: Leo Margolis
url: http://www.margollo.github.io

GAP: ">=4.7"

Expand All @@ -28,7 +36,7 @@ packageinfo: https://gap-packages.github.io/modisom/PackageInfo.g

downloads:
- name: .tar.gz
url: https://github.com/gap-packages/modisom/releases/download/v2.5.4/modisom-2.5.4.tar.gz
url: https://github.com/gap-packages/modisom/releases/download/v3.0.0/modisom-3.0.0.tar.gz

abstract: |
The <span class="pkgname">ModIsom</span> package contains various methods for computing with nilpotent associative algebras. In particular, it contains a method to determine the automorphism group and to test isomorphis of such algebras over finite fields and of modular group algebras of finite p-groups, and it contains a nilpotent quotient algorithm for finitely presented associative algebras and a method to determine Kurosh algebras.
Expand All @@ -40,30 +48,31 @@ keywords: |
modular isomorphism problem, automorphism group, isomorphism testing, nilpotent algebras, nilpotent quotient, Kurosh algebras.
citeas: |
<p class='BibEntry'>
[<span class='BibKey'>EK23</span>] <b class='BibAuthor'>Eick, B. and Konovalov, O.</b>,
[<span class='BibKey'>EGKMM24</span>] <b class='BibAuthor'>Eick, B., Garcia-Lucas, D., Konovalov, O., Margolis, L. and Moede, T.</b>,
<i class='BibTitle'>ModIsom, Computing automorphisms and checking isomorphisms for modular group algebras of finite p-groups,
Version 2.5.4</i>
(<span class='BibYear'>2023</span>)<br />
(<span class='BibNote'>Refereed GAP package</span>),
Version 3.0.0</i>
(<span class='BibYear'>2024</span>)<br />
(<span class='BibNote'>GAP package</span>),
<span class='BibHowpublished'><a href="https://gap-packages.github.io/modisom/">https://gap-packages.github.io/modisom/</a></span>.
</p>
bibtex: |
@misc{ ModIsom2.5.4,
author = {Eick, B. and Konovalov, O.},
@misc{ ModIsom,
author = {Eick, B. and Garcia\texttt{\symbol{45}}Lucas, D. and
Konovalov, O. and Margolis, L. and Moede, T.},
title = {{ModIsom}, Computing automorphisms and checking
isomorphisms for modular group algebras of finite
p-groups, {V}ersion 2.5.4},
month = {Feb},
year = {2023},
note = {Refereed GAP package},
p\texttt{\symbol{45}}groups, {V}ersion 3.0.0},
month = {Sep},
year = {2024},
note = {GAP package},
howpublished = {\href {https://gap-packages.github.io/modisom/}
{\texttt{https://gap-packages.github.io/}\discretionary
{\texttt{https://gap\texttt{\symbol{45}}packages.github.io/}\discretionary
{}{}{}\texttt{modisom/}}},
keywords = {modular isomorphism problem; automorphism group;
isomorphism testing; nilpotent algebras; nilpotent
quotient; Kurosh algebras},
printedkey = {EK23}
printedkey = {EGKMM24}
}
57 changes: 41 additions & 16 deletions htm/CHAP001.htm
Original file line number Diff line number Diff line change
Expand Up @@ -4,8 +4,10 @@
<h1>1 Introduction</h1><p>
<p>
This package contains various algorithms related to finite dimensional
nilpotent associative algebras. We first give a brief introduction to
these algebras and then an overview of the main algorithms.
nilpotent associative algebras. It also contains many group-theoretical
functions related to the Modular Isomorphism Problem.
We first give a brief introduction to finite dimensional
nilpotent algebras and then an overview of the main algorithms.
<p>
<p>
<hr>Associative algebras and nilpotency
Expand Down Expand Up @@ -52,7 +54,7 @@ <h1>1 Introduction</h1><p>
in <a href="biblio.htm#Eic07"><cite>Eic07</cite></a> which allow the determination of the automorphism group
<i>Aut</i>(<i>A</i>) and a <strong>canonical form</strong> <i>Can</i>(<i>A</i>).
<p>
The automorphism group is given by generators and it represented as a
The automorphism group is given by generators and is represented as a
subgroup of <i>GL</i>(<i>dim</i>(<i>A</i>), <i>F</i>). Also the order of <i>Aut</i>(<i>A</i>) is available.
<p>
A canonical form <i>Can</i>(<i>A</i>) for <i>A</i> is a nilpotent structure constants
Expand All @@ -61,39 +63,62 @@ <h1>1 Introduction</h1><p>
isomorphism problem.
<p>
<p>
<hr>The modular isomorphism problem
<hr>The Modular Isomorphism Problem
<p>
The modular isomorphism problem asks whether <b>F</b><i>G</i> &#8773; <b>F</b><i>H</i> implies
that <i>G</i> &#8773; <i>H</i> for two <i>p</i>-groups <i>G</i> and <i>H</i> and <b>F</b> the field with <i>p</i>
elements. This problem is still open, despite various efforts towards
proving the claim or finding counterexamples to it.
The modular isomorphism problem asks whether an isomorphism of algebras <b>F</b><sub><i>p</i></sub> <i>G</i> &#8773; <b>F</b><sub><i>p</i></sub> <i>H</i> implies
an isomorphism of groups <i>G</i> &#8773; <i>H</i> for two <i>p</i>-groups <i>G</i> and <i>H</i> and <b>F</b><sub><i>p</i></sub> the field with <i>p</i>
elements. This problem was open for a long time until first counterexamples
for the prime <i>p</i>=2 were found in <a href="biblio.htm#GLMdR22"><cite>GLMdR22</cite></a>. It remains open for odd
primes and many other interesting classes of groups.
<p>
Computational approaches have been used to investigate the modular isomorphism
problem. Based on an algorithm by Roggenkamp and Scott <a href="biblio.htm#RS93"><cite>RS93</cite></a>, Wursthorn
<a href="biblio.htm#Wur93"><cite>Wur93</cite></a> described an algorithm for checking the modular isomorphism
problem; that is, he described an algorithm for checking whether two modular
group algebras <b>F</b><i>G</i> and <b>F</b><i>H</i> are isomorphic. This algorithm has been
implemented in C by Wursthorn and has been used applied to the groups of
group algebras <b>F</b><sub><i>p</i></sub> <i>G</i> and <b>F</b><sub><i>p</i></sub> <i>H</i> are isomorphic, where <i>G</i> and <i>H</i> are finite
<i>p</i>-groups. This algorithm has been
implemented in C by Wursthorn and has been applied to the groups of
order dividing 2<sup>7</sup> without finding a counterexample, see <a href="biblio.htm#BKRW99"><cite>BKRW99</cite></a>.
The implementation of Wursthorn appears lost, but is in any case not publicly
available.
<p>
<p>
This package contains an implementation of the new algorithm described in
<a href="biblio.htm#Eic07"><cite>Eic07</cite></a> for checking isomorphism of modular group algebras. It is based
on the fact that the Jacobson radical <i>J</i>(<i>FG</i>) is nilpotent if <i>FG</i> is a
modular group algebra. Hence the automorphism group and canonical form
modular group algebra for <i>G</i> a finite <i>p</i>-group and <i>FG</i> is isomorphic to <i>FH</i> if and only if the radicals
<i>J</i>(<i>FG</i>) and <i>J</i>(<i>FH</i>) are isomorphic. Hence the automorphism group and canonical form
algorithm of this package apply and can be used to solve the isomorphism
problem for modular group algebras.
problem for modular group algebras of finite <i>p</i>-groups. Note that in this setting the Jacobson radical of the group algebra <i>FG</i> equals its augmentation ideal.
<p>
The methods of this package have been used to check the modular isomorphism
The methods of this package have been used to study the modular isomorphism
problem for the groups of order dividing 3<sup>6</sup> and 2<sup>8</sup> (<a href="biblio.htm#Eic07"><cite>Eic07</cite></a>) and
for the groups of order 2<sup>9</sup> (<a href="biblio.htm#EKo11"><cite>EKo11</cite></a>).
for the groups of order 2<sup>9</sup> (<a href="biblio.htm#EKo11"><cite>EKo11</cite></a>). It was later used to study also
groups of order 3<sup>7</sup> and 5<sup>6</sup> (<a href="biblio.htm#MM22"><cite>MM22</cite></a>).
<p>
<p>
A property of a group <i>G</i> is called <strong><i>F</i>-invariant</strong>, if an isomorphism of
<i>F</i>-algebras <i>FG</i> &#8773; <i>FH</i> implies the same property for <i>H</i>. In the context
of the Modular Isomorphism Problem, if <i>G</i> is a finite <i>p</i>-group, then an
<b>F</b><sub><i>p</i></sub>-invariant is simply called
<strong>invariant</strong>. Many invariants of <i>G</i> are known and the package provides
functions for them, as well as programs which easily allow to compare all
the implemented invariants quickly for a given list of groups.
<p>
<p>
It also remains open, if replacing the field <b>F</b><sub><i>p</i></sub> in the Modular Isomorphism
Problem with a bigger field of characteristic <i>p</i> will change the outcome
of the problem for a given pair of groups. The package includes several
functions which allow to investigate this question by applying the algorithm
for the same groups varying the field.
<p>
<p>
<hr>A nilpotent quotient algorithm
<p>
Given a finitely presented associative algebra <i>A</i> over an arbitrary
field <i>F</i>, this package contains an algorithm to determine a nilpotent
structure constants table for the class-<i>c</i> nilpotent quotient of <i>A</i>.
structure constants table for the class-<i>c</i> nilpotent quotient of <i>A</i>,
i.e. the algebra <i>A</i>/<i>A</i><sup><i>c</i>+1</sup>.
See <a href="biblio.htm#Eic11"><cite>Eic11</cite></a> for details on the underlying algorithm.
<p>
<p>
Expand All @@ -117,5 +142,5 @@ <h1>1 Introduction</h1><p>
<p>
[<a href = "chapters.htm">Up</a>] [<a href ="CHAP002.htm">Next</a>] [<a href = "theindex.htm">Index</a>]
<P>
<address>ModIsom manual<br>February 2023
<address>ModIsom manual<br>September 2024
</address></body></html>
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