Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T13:47:47.395Z Has data issue: false hasContentIssue false
  • English
  • Français

Π′-closure of finite Π-solvable groups

Published online by Cambridge University Press:  09 April 2009

Zvi Arad
Zvi Arad
Affiliation:
Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The purpose of this paper is to present a proof of the following theorem: Suppose Π is a set of dd primes, G is a finite Π-solvable group, and A is a nilpotent Π-subgroup of maximal order of G. Then G has a normal Π-complement, if and only if NG(ZJ(A)) has a normal Π-complement. (J(A) is the Thompson subgroup of A.)

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1976 , pp. 118 - 119
Copyright
Copyright © Australian Mathematical Society 1976

References

Arad, Z. and Glauberman, G. (to appear), ‘A characteristic subgroup of a group of odd order’, Pacific J. Math.Google Scholar
Bialostocki, B. (to appear) ‘On products of two nilpotent subgroups of a finite group’, Israel J. Math.Google Scholar
Feit, W. and Thompson, J. G. (1963), ‘Solvability of groups of odd order’, Pacific J. Math. 13, 775–1029.CrossRefGoogle Scholar
Gorenstein, D. (1968), Finite Groups (Harper and Row, New York, 1968).Google Scholar
Mann, A. (1971), ‘Injectors and normal subgroups of finite groups’, Israel J. Math. 9, 554–558.Google Scholar