Baumann-components of finite groups of characteristic p, the W(B)-theorem

Abstract

This paper completes the investigation of finite ▪-groups of characteristic p in terms of their Baumann components we began in [5] and [6].In this paper we define for each finite p-group B a non-trivial characteristic subgroup ▪ and for each finite ▪-group G of characteristic p with ▪, subnormal subgroups of G called Baumann blocks of G.We prove that ▪, where ▪ is the normal subgroup generated by the Baumann blocks of G. Moreover, we give the exact structure of the Baumann blocks of G and show that any two distinct Baumann blocks centralize each other.