Finite Soluble Groups [HB 23]

New Features:

• A function for computing normal complements (NormalComplements) has been implemented.
• The functions ExtGenerators (G, U) and HomGenerators (G, U) have been introduced to construct explicit generators for Ext (G/G', U), respectively Hom (H₂ (G), U), as cocyclic matrices where U is abelian.
• The function RepresentativeCocyles has been introduced for computing representative cocycles from G to abelian U as cocyclic matrices.
• The new functions CentralExtension and CentralExtensions return central extensions of U by G determined by cocyclic matrices.
• The function CentralExtensionProcess (G, U) has been introduced for creating a process for forming all central extensions of abelian U by G. Related functions are NextExtension and IsEmpty.