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On groups with all subgroups almost subnormal

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Eloisa Detomi
Eloisa Detomi
Affiliation:
Dipartimento di Matematica, Facoltà di Ingegneria, Università degli Studi di Brescia, via Valotti 9, 25133 Brescia, Italia e-mail: detomi@ing.unibs.it
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Abstract

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In this paper we consider groups in which every subgroup has finite index in the nth term of its normal closure series, for a fixed integer n. We prove that such a group is the extension of a finite normal subgroup by a nilpotent group, whose class is bounded in terms of n only, provided it is either periodic or torsion-free.

MSC classification

Secondary: 20E15: Chains and lattices of subgroups, subnormal subgroups 20F19: Generalizations of solvable and nilpotent groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 2 , October 2004 , pp. 165 - 174
Copyright
Copyright © Australian Mathematical Society 2004

References

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