∏’-Closure of finite ∏-solvable groups

Zvi Arad

doi:10.1017/S1446788700016992

∏’-Closure of finite ∏-solvable groups

Zvi Arad

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	118-119
Number of pages	2
Journal	Journal of the Australian Mathematical Society
Volume	21
Issue number	1
DOIs	https://doi.org/10.1017/S1446788700016992
State	Published - Feb 1976

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

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

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∏’-Closure of finite ∏-solvable groups

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