Abstract: Let G be a finite group, and let F be a formation of
finite group. We say that a subgroup H of G is p F -normal in G if
there exists a normal subgroup T of G such that HT is a permutable
Hall subgroup of G and G G (H
Abstract: A square matrix over the complex field with non- negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful representation of G by quasi-permutation matrices over the rationals and the complex numbers are denoted by q(G) and c(G) respectively. Finally r (G) denotes the minimal degree of a faithful rational valued complex character of C. The purpose of this paper is to calculate q(G), c(G) and r(G) for the group S L(2, q) when extended by a certain group of order two.
Abstract: In this paper, we investigate the influence of Ssemipermutable and weakly S-supplemented subgroups on the pnilpotency of finite groups. Some recent results are generalized.