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On certain subgroups of a join of subnormal subgroups

Published online by Cambridge University Press:  18 May 2009

Howard Smith
Howard Smith
Affiliation:
Department of Pure Mathematics, University College, Cardiff
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1. Introduction: Suppose the group G is generated by subnormal subgroups H and K, and that A, B are normal subgroups of finite index in H, Krespectively. The following question has been asked by J. C. Lennox: Under what circumstances is the subgroupJ = (A, B) subnormal in G? In particular, it is of interest to know when J has finite index in G, for, if this is the case, we may factor out by the normal core of J in G and apply Wielandt's theorem on joins of subnormal subgroups of finite groups [11] to deduce that J is subnormal in G. Here we prove the following result.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 1 , January 1984 , pp. 103 - 105
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

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