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Supplementation in groups

Published online by Cambridge University Press:  07 August 2001

Luise-Charlotte Kappe  and
Joseph Kirtland
Luise-Charlotte Kappe
Affiliation:
Department of Mathematical Sciences, SUNY Binghamton, Binghamton NY, 13902-6000, USA. Email:[email protected]
Joseph Kirtland
Affiliation:
Department of Mathematics, Marist College, Poughkeepsie, NY 12601, USA Email:[email protected]
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Abstract

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In this paper, groups are investigated in which all subgroups, all normal subgroups, or all characteristic subgroups have a proper supplement. This supplement can be either an arbitrary subgroup, a normal or a characteristic subgroup, resulting in nine classes of groups. Properties of these classes are studied such as containment and closure properties, and characterizations for several of these classes are given.

1991 Mathematics Subject Classification Primary 20E34, Secondary 20E15.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 1 , March 2000 , pp. 37 - 50
Copyright
2000 Glasgow Mathematical Journal Trust