Versio 3.0.0

COPYRIGHT

@@ -4,8 +4,11 @@ The principal author and copyright holder of the ModIsom package is
 Bettina Eick.
 
 This package contains additional code and other contributions by:
+- Diego Garcia-Lucas
 - Max Horn
 - Olexandr Konovalov
+- Leo Margolis
+- Tobias Moede
 
 License
 

PackageInfo.g

@@ -5,8 +5,8 @@
 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 := "26/02/2024", # dd/mm/yyyy format
 License := "GPL-2.0-or-later",
 
 Persons := [
@@ -26,21 +26,70 @@ 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",
     IsAuthor      := false,
     IsMaintainer  := true,
     Email         := "[email protected]",
-    WWWHome       := "https://olexandr-konovalov.github.io/",
+    WWWHome       := "https://alex-konovalov.github.io/",
     PostalAddress := Concatenation( [
                      "School of Computer Science\n",
                      "University of St Andrews\n",
                      "Jack Cole Building, North Haugh,\n",
                      "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)",

README.md

@@ -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
@@ -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.
+# modisom3

VERSION

@@ -1 +1 @@
-2.5.4
+3.0.0

changes.txt

@@ -0,0 +1,80 @@
+Overview of files changeg in respect to ModIsom 2.5.3:
+
+ModIsomExt refers to a GAP package written by Leo Margolis and Tobias Moede the functionality of which is now included in this package, cf. https://www.tu-braunschweig.de/index.php?eID=dumpFile&t=f&f=114036&token=7391a74bb71a93524f0dc24d07e5330c3d3cdf6e and https://doi.org/10.1016/j.jaca.2022.100001.
+
+Changed:
+- detbins.gi: 
+-- New invariants and new functions for all fields. Also new functions which do not need the order as input. 
+-- Some of the existing functions now give more information, e.g. ConjugacyClassInfo or SandlingInfo
+-- Many of the functions are now documented. This concerns both, new and unchanged functions
+
+- checkbin.gi:  
+-- Corrected mistake in main function as done in ModIsomExt. Basically, just copied the file from ModIsomExt
+-- New functionality which allows application to bigger fields
+-- Print info on time etc. as in ModIsomExt 
+
+- fprint.gi: corrected mistake in function PowerBasisWeights as done in ModIsomExt
+
+New files:
+- collect.gi as given in ModIsomExt. Function to efficiently compute with Jennings bases in Loewy series quotients of the augmentation ideal
+- Jennings bound functions which in ModIsomExt are in detbins.gi into new files jenningsBound.g and jenningsConjecture.g
+- kernelsize.gi: to compute kernel sizes of power maps
+- tabletoalgebrandback.gi: functions which allow to convert hence and forth between elements in the group algebra (or rather the augmentation ideal) and the corresponding table
+- detbinsRT.gi: for the ring-theoretic functions of detbins.gi in ModIsom
+
+Technical differences between ModIsom and ModIsomExt:
+- ModIsom uses BindGlobal while ModIsomExt uses InstallMethod. --> Has been changed everywhere to BindGlobal
+- Documentation is generated differently. ModIsom uses GAPMacro --> Fused 
+
+-------------------------------------------------
+------------------------------------------------
+
+Concrete changes:
+
+detbins.gi:
+- RefinBins from ModIsomExt (i.e. to refine lists of groups and not only of ids)
+- MIPConjugcayClassInfo from ModIsomExt (i.e. with the parameter of Parmenter-Polcino Milies)
+- MIPJenningsInfo from ModIsomExt (i.e. incorporating Hertweck's G/D4(G) and better id recognition)
+- MIPSandlingInfo from ModIsomExt (i.e. incorporating Baginski/Margolis-Moede on small group rings)
+- BaginskiInfo from ModIsomExt, implementing Baginski99-results
+- CenterDerivedInfo from ModIsomExt
+- FrattiniInfo from ModIsomExt
+- JenningsDerivedInfo from ModIsomExt
+- BaginskiCarantiInfo from ModIsomExt
+- NilpotencyClassInfo from ModIsomExt
+- DimensionTwoCohomology from ModIsomExt
+
+- MIPJenningsInfoAllFields, only subsequent Jennings quotients
+- DimensionSecondHochschild, computes dimension of second Hochschild cohomology group
+- IsCoveredByTheory extended from ModIsomExt with various new results
+- IsCoveredByTheoryAllFields new function
+- Theorem41MS22 new function for result from Margolis-Stanojkovski
+- MaximalAbelianDirectFactor and MaximalElementaryAbelianDirectFactor new functions for canceling factors
+- AgemoInvariantAllM and OmegaInvariantAllM and AgemoCenterInvariantAllM and NormalSubgroupsInfo new functions based on Garcia-Lucas and Margolis-Sakurai-Stanojkovski
+- CyclicDerivedInfo and CyclicDerivedInfoAllFields new functions based on Garcia-Lucas-Del Rio-Stanojkovski and Garcia-Lucas-Del Rio
+- MIPBinsByGTInternal changed from ModIsomExt to incorporate new invariants and option to shut off cohomology calculations
+- MIPBinsByGT changes to 2-4 variables and with new invariants
+- MIPBinsByGTAllFieldsInternal and MIPBinsByGTAllFields new functions for all fields
+- MIPSplitGroupsByGroupTheoreticalInvariants and MIPSplitGroupsByGroupTheoreticalInvariantsNoCohomology and MIPSplitGroupsByGroupTheoreticalInvariantsAllFields and MIPSplitGroupsByGroupTheoreticalInvariantsAllFieldsNoCohomology new user friendly functions which only need list of groups as input
+
+
+checkbin.gi:
+- MIPBinSplit from ModIsomExt with change to allow to increase field
+- MIPSplitGroupsByAlgebras new user friendly function with input list of groups (and optional number to increase field)
+
+fprint.gi: correction of mistake in PowerBasisWeights as already done in ModIsomExt
+
+collect.gi: like in ModIsomExt + new user friendly function ModIsomTable
+
+detbinsRT.gi: functions in the second half of the old checkbin.gi
+
+kernelsize.gi: compute kernel size of power map
+
+jenningsBounds.g: functions on Jennings bound from ModIsomExt
+
+tabletoalgebrandback.gi: MIPElementTableToAlgebra and MIPElementAlgebraToTable functions to convert elements between group algebra and table
+
+Manual:
+- many of the new functions have been documented as well as the changes in the previous functions. Also some functions which remain unchanged are now documented
+
+

doc/autiso.tex

@@ -9,7 +9,7 @@
 
 Let $T$ be a nilpotent table over $F$. The following function can be used 
 to determine the automorphism group of the algebra described by $T$. The
-automorphism group is determined as subgroup of $GL(T.dim, T.fld)$ given 
+automorphism group is determined as subgroup of $GL(T\.dim, T\.fld)$ given 
 by generators and its order. There is a variation available to determine
 the automorphism group of a modular group algebra $FG$, where $F$ is a finite
 field and $G$ is a $p$-group.

doc/intro.tex

@@ -9,8 +9,10 @@
 \Chapter{Introduction}
 
 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.
 \medskip
 
 {\bf Associative algebras and nilpotency}
@@ -26,7 +28,8 @@
 
 An associative algebra $A$ is *nilpotent* if its *power series* terminates
 at the trivial ideal of $A$; that is
-$$ A > A^2 > \ldots > A^c > A^{c+1} = \{0\} $$
+$$
+A > A^2 > \ldots > A^c > A^{c+1} = \{0\} $$
 where $A^j$ is the ideal of $A$ generated by all products of length 
 at least $j$. The length $c$ of the power series is also called the 
 *class* of $A$ and the dimension of $A/A^2$ is the *rank* of $A$. Note
@@ -57,7 +60,7 @@
 in \cite{Eic07} which allow the determination of the automorphism group 
 $Aut(A)$ and a *canonical form* $Can(A)$. 
 
-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 $GL(dim(A), F)$. Also the order of $Aut(A)$ is available.
 
 A canonical form $Can(A)$ for $A$ is a nilpotent structure constants 
@@ -67,39 +70,62 @@
 isomorphism problem. 
 \medskip
 
-{\bf The modular isomorphism problem}
+{\bf The Modular Isomorphism Problem}
 
-The modular isomorphism problem asks whether $\F G \cong \F H$ implies
-that $G \cong H$ for two $p$-groups $G$ and $H$ and $\F$ the field with $p$
-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 $\F_p G \cong \F_p H$ implies
+an isomorphism of groups $G \cong H$ for two $p$-groups $G$ and $H$ and $\F_p$ the field with $p$
+elements. This problem was open for a long time until first counterexamples
+for the prime $p=2$ were found in \cite{GLMdR22}. It remains open for odd
+primes and many other interesting classes of groups.
 
 Computational approaches have been used to investigate the modular isomorphism
 problem. Based on an algorithm by Roggenkamp and Scott \cite{RS93}, Wursthorn
 \cite{Wur93} described an algorithm for checking the modular isomorphism
 problem; that is, he described an algorithm for checking whether two modular
-group algebras $\F G$ and $\F H$ are isomorphic. This algorithm has been
-implemented in C by Wursthorn and has been used applied to the groups of
+group algebras $\F_p G$ and $\F_p H$ are isomorphic, where $G$ and $H$ are finite
+$p$-groups. This algorithm has been
+implemented in C by Wursthorn and has been applied to the groups of
 order dividing $2^7$ without finding a counterexample, see \cite{BKRW99}.
+The implementation of Wursthorn appears lost, but is in any case not publicly
+available.
 \medskip
 
 This package contains an implementation of the new algorithm described in
 \cite{Eic07} for checking isomorphism of modular group algebras. It is based
 on the fact that the Jacobson radical $J(FG)$ is nilpotent if $FG$ is a 
-modular group algebra. Hence the automorphism group and canonical form 
+modular group algebra for $G$ a finite $p$-group and $FG$ is isomorphic to $FH$ if and only if the radicals
+$J(FG)$ and $J(FH)$ 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 $p$-groups. Note that in this setting the Jacobson radical of the group algebra $FG$ equals its augmentation ideal.
 
-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 $3^6$ and $2^8$ (\cite{Eic07}) and
-for the groups of order $2^9$ (\cite{EKo11}).
+for the groups of order $2^9$ (\cite{EKo11}). It was later used to study also 
+groups of order $3^7$ and $5^6$ (\cite{MM22}).
+\medskip
+
+A property of a group $G$ is called *$F$-invariant*, if an isomorphism of
+$F$-algebras $FG \cong FH$ implies the same property for $H$. In the context
+of the Modular Isomorphism Problem, if $G$ is a finite $p$-group, then an 
+$\F_p$-invariant is simply called 
+*invariant*. Many invariants of $G$ 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.
+\medskip
+
+It also remains open, if replacing the field $\F_p$ in the Modular Isomorphism
+Problem with a bigger field of characteristic $p$ 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.
 \medskip
 
 {\bf A nilpotent quotient algorithm}
 
 Given a finitely presented associative algebra $A$ over an arbitrary
 field $F$, this package contains an algorithm to determine a nilpotent
-structure constants table for the class-$c$ nilpotent quotient of $A$. 
+structure constants table for the class-$c$ nilpotent quotient of $A$,
+i.e. the algebra $A/A^{c+1}$. 
 See \cite{Eic11} for details on the underlying algorithm.
 \medskip