5 research outputs found
Finite Groups Having Nonnormal T.I. Subgroups
In the present paper, the structure of a finite group having a nonnormal
T.I. subgroup which is also a Hall -subgroup is studied. As a
generalization of a result due to Gow, we prove that is a Frobenius
complement whenever is -separable. This is achieved by obtaining the
fact that Hall T.I. subgroups are conjugate in a finite group. We also prove
two theorems about normal complements one of which generalizes a classical
result of Frobenius
Character free proofs for two solvability theorems due to Isaacs
We give character-free proofs of two solvability theorems due to Isaacs
Cyclic intersections and control of fusion
Let H be a subgroup of a finite group G, and suppose that H contains a Sylow p-subgroup P of G. Write N=NG(H)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, and assume that the Sylow p-subgroups of H boolean AND Hg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} are cyclic for all elements g is an element of G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} not lying in N. We show that in this situation, N controls G-fusion in P