pi-blocks of pi-separable groups. I
Several authors have attempted to defined \(\pi\)-blocks for finite groups, \(\pi\) a set of primes, as a generalization of p-blocks, p a prime. It seems that the theory of \(\pi\)-blocks for arbitrary finite groups can only to a certain point, exploring formal analogies of some kinds. To go further it seems necessary to make assumptions on the \(\pi\)-structures of the groups considered. The present author considers \(\pi\)-separable groups. Under this strong assumption he obtains very nice and interesting results for the \(\pi\)-blocks. The approach is based on results of Isaacs, which are presented in a suitable way in {\S}1. Then {\S}2 contains the author's definition of \(\pi\)-blocks in \(\pi\)-separable groups, and its relation to other definitions is discussed. This paper is the first of a series.
scientific article; zbMATH DE number 3957406
scientific article