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A note on subnormality

Published online by Cambridge University Press:  17 April 2009

T.A. Peng
T.A. Peng
Affiliation:
Department of Mathematics, University of Singapore, Singapore.
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Abstract

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Let H be a subgroup of a finite group G and let S be a set of generators of H. We prove that if G is soluble, then H is subnormal in G if and only if there exists an integer n such that for each g in G and a in S the commutator lies in H. This criterion for subnormality is also valid for soluble groups satisfying the maximal or the minimal condition on subgroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 1 , August 1976 , pp. 59 - 64
Copyright
Copyright © Australian Mathematical Society 1976

References

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