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A note on locally soluble, normal closures of cyclic subgroups

Published online by Cambridge University Press:  18 May 2009

Howard Smith
Howard Smith
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, U.S.A.
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This brief note has the threefold purpose of improving on an earlier theorem of the author [4], gathering together some results on normal closures (with rank restrictions) which are more or less implicit in the literature and providing a few examples which indicate the impossibility of improving these results in one way or another. The proofs are mostly routine and usually omitted. Most of the relevant background material can be found in [3], and references to these results will often indicate that minoradditional details (an easy induction, for example) are required. Throughout, 〈x〉G will denote the normal closure of the subgroup 〈x〉 of the group G. The usual notation is used for upper central and derived series.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 1 , January 1994 , pp. 33 - 36
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

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