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Subnormal subgroups in direct products of groups

Published online by Cambridge University Press:  09 April 2009

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1987

References

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[8]Robinson, D. J. S., A course in the theory of groups (Springer, Berlin, 1982).CrossRefGoogle Scholar
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