J Austral Math Soc Ser A 45 pp389--400, 1988.

Subnormal Embedding of Relatively Complete Groups

Hermann Heineken and Panagiotis Soules

Abstract

In this paper we show that a group A is embedded in any finite group G as a subnormal subgroup with low degree of complication, provided that the automorphism group of A satisfies a condition depending on some Fitting class (which coincides with completeness for the Fittign class of all groups). A criterion is given for these groups as to whether they can be embedded subnormally in the commutator subgroup of some finite group or not.

1980 AMS Subject Classification (1985 Revision): 20D35, 20D45, 20D10

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Authors

Hermann Heineken

Mathematisches Institut, Universität Würzburg, Würzburg, Federal Republic of Germany.

Panagiotis Soules

Department of Mathematics, University of Athens, Athens, Greece.