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Splitting theorems in abelian-by-hypercyclic groups

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

M. J. Tomkinson
M. J. Tomkinson
Affiliation:
Department of Mathematics University of GlasgowGlasgow G12 8QWScotland
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Abstract

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If is a saturated formation of finite soluble groups and G is a finite group whose -residual A is abelian then it is well known that G splits over A and the complements are conjugate. Hartley and Tomkinson (1975) considered the special case of this result in which is the class of nilpotent groups and obtained similar results for abelian-by-hypercentral groups with rank restrictions on the abelian normal subgroup. Here we consider the super-soluble case, obtaining corresponding results for abelian-by-hypercyclic groups.

MSC classification

Secondary: 20E15: Chains and lattices of subgroups, subnormal subgroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1978 , pp. 71 - 91
Copyright
Copyright © Australian Mathematical Society 1978

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