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Subnormal subgroups in direct products of groups

Part of: Structure and classification of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Peter Hauck
Peter Hauck
Affiliation:
Mathematisches InstitutAlbert-Ludwigs-Universität Albertstraβe 23 b D-7800 Freiburg Federal Republic of, Germany
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Abstract

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A group G is called normally (subnormally) detectable if the only normal (subnormal) subgroups in any direct product G1 × … × Gn of copies of G are just the direct factors Gi. We give an internal characterization of finite subnormally detectable groups and obtain analogous results for associative rings and for Lie algebras. The main part of the paper deals with a study of normally detectable groups, where we verify a conjecture of T. O. Hawkes in a number of special cases.

MSC classification

Secondary: 20E15: Chains and lattices of subgroups, subnormal subgroups 20D35: Subnormal subgroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 2 , April 1987 , pp. 147 - 172
Copyright
Copyright © Australian Mathematical Society 1987

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