J Austral Math Soc Ser A 48 pp171--198, 1990.

Radicals and Subdirect Decompositions of W-groups

R. Mlitz and S. Veldsman

Abstract

Starting with a class M of W-groups, necessary and sufficient conditions on M are given to ensure that the corresponding Hoehnke radical r (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 rN ÇI Í rI and lastly, have both a hereditary radical and semisimple class or satisfies rN ÇI = rI.

1980 AMS Subject Classification (1985 Revision): 08A05, 16A21

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Authors

R. Mlitz

Technische Universität Wien, Institut für Angewandte und, Numerische Mathematik, A-1040 Wien, Austria.

S. Veldsman

Department of Mathematics, University of Port Elizabeth, P.O. Box 1600, Port Elizabeth, South Africa.