Permutation Groups [HB 18]

 

New Features:

• Major improvements to the techniques for computing subgroups using the Subgroups family of functions have been introduced. It is now possible to compute subgroups in very much larger groups than before.
• A new very powerful algorithm for finding maximal subgroups in the case of a non-soluble group has been installed. This algorithm, developed by Derek Holt, reduces the problem of finding maximal subgroups to that of knowing the maximals of the non-abelian composition factors (and their automorphism groups).
• The ability to compute maximal subgroups is used as the basis of an algorithm to compute subgroups of small index in a large permutation group (function LowIndexSubgroups).
• The function AutomorphismGroup determines the full automorphism group of a permutation group.
• Isomorphism of permutation groups may be tested using the function IsIsomorphic. Note that this tests for abstract group isomorphism, not permutation isomorphism.
• The function OrbitRepresentatives has been introduced to determine just the orbit lengths and representatives; it is more space-efficient than the general-purpose Orbits.
• The new function IsInnerAutomorphism has been provided.
• The functions ElementaryAbelianQuotient, pQuotient and NilpotentQuotient are now available for permutation groups.

Bug fixes:

• A bug in DerivedSeries has been fixed. The bug was responsible for incorrect results produced by IsSimple and some other functions.