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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.
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Abstract

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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.)

Information

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

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