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Subnormal embedding of relatively complete groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Hermann Heineken  and
Panagiotis Soules
Hermann Heineken
Affiliation:
Mathematisches Institut, Universität Würzburg, Würzburg Federal Republic of, Germany
Panagiotis Soules
Affiliation:
Department of Mathematics, University of Athens, Athens, Greece
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Abstract

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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 Fitting 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.

MSC classification

Secondary: 20D35: Subnormal subgroups 20D45: Automorphisms 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 3 , December 1988 , pp. 389 - 400
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Blessenohl, D. and Gaschütz, W., ‘Über normale Schunck—und Fittingklassen”, Math. Z. 118 (1970), 1–8.Google Scholar
[2]Gagen, T. M., ‘Some finite solvable groups with no outer automorphisms’, J. Algebra 65 (1980), 84–94.Google Scholar
[3]Heineken, H. and Lennox, J. C., ‘The subnormal embedding of complete groups”, J. Algebra 90 (1984), 435–445.Google Scholar
[4]Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[5]Wielandt, H., ‘Vertauschbare nachinvariante Untergruppen”, Abh. Math. Sem. Univ. Hamburg 21 (1957), 55–62.Google Scholar