Finitely Presented Groups [HB 26]

Changes:

• A new method has been implemented for computing preimages of submodules of a K[G]-module M, defined by an elementary abelian section of a finitely presented group G. The new approach yields significantly reduced running times and presents an important improvement to the tools for constructing normal subgroups of finitely presented groups.
• The possibility of imposing time limits has been provided for the functions LowIndexSubgroups and LowIndexSubgroupsProcess. This gives the user increased control when employing these functions in combination with other strategies in the search for subgroups satisfying certain properties.

New features:

• A new function, Homomorphisms, computing equivalence classes of homomorphisms from a finitely presented group F to a permutation group G modulo a user specified subgroup of the automorphism group of G has been provided. The efficient implementation of the underlying backtrack search allows to compute quotients of order 10⁸ or 10⁹ for finitely presented groups with few generators in very reasonable time. An interactive version of this algorithm exists as well.
• Building on the above machinery, functions have been implemented to enumerate all epimorphisms of a finitely presented group onto any simple group having order less than 10⁹. The main function is SimpleQuotients and, in addition, a process version is provided.
• The new function IsPerfect, testing whether a finitely presented group is perfect, has been provided.
• The function AbelianQuotientInvariants has been improved by the use of new sparse matrix techniques.

Bug fixes:

• A bug in simplifying presentations using Tietze transformations has been fixed. This problem affected various other functions making indirect use of Tietze transformations.
• A problem with the sub<G| f> constructor, creating a subgroup of G as point stabiliser of the transitive permutation representation f was fixed. It is now checked that f is transitive and invalid data is reported as runtime error.