Abelian invariants and a reduction theorem for the modular isomorphism problem

Abstract

We show that elementary abelian direct factors can be disregarded in the study of the modular isomorphism problem. Moreover, we obtain four new series of abelian invariants of the group base in the modular group algebra of a finite $p$-group. Finally, we apply our results to new classes of groups.

arXiv comment24 pages, proof of Theorem 2.4 modified from previous version

References in corpus (4)

• The isomorphism problem for group algebras: a criterion
• The modular isomorphism problem for finite $p$-groups with a cyclic subgroup of index $p^2$
• On the Modular Isomorphism Problem for groups of class 3 and obelisks
• Cohomological uniqueness, Massey products and the modular isomorphism problem for 2-groups of maximal nilpotency class