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Radicals and subdirect decompositions of Ω-groups

Part of: Algebraic structures

Published online by Cambridge University Press:  09 April 2009

R. Mlitz  and
S. Veldsman
R. Mlitz
Affiliation:
Technische Universität WienInstitut fü Angewandte und Numerische A-1040 Wien, Austria
S. Veldsman
Affiliation:
Department of Mathematics, University of Port ElizabethP. O. Box 1600 6000 Port Elizabeth, South Africa
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Abstract

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Starting with a class ℳ of Ω-groups, necessary and sufficient conditions on ℳ are given to ensure that the corresponding Hoehnke radical ρ (determined by the subdirect closure of ℳ as semisimple class) is a radical in the sense of Kurosh and Amitsur; has a hereditary semisimple class; satisfies the ADS-property; has a hereditary radical class or satisfies ρN ∩ I ⊆ ρI and lastly, have both a hereditary radical and semisimple class or satisfies ρN ∩ I = ρI.

MSC classification

Secondary: 08A05: Structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 2 , April 1990 , pp. 171 - 198
Copyright
Copyright © Australian Mathematical Society 1990

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