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On groups in which every subgroup is subnormal of defect at most three

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Gunnar Traustason
Gunnar Traustason
Affiliation:
Christ Church Oxford OX1 1DPEngland e-mail: [email protected]
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Abstract

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In this paper we study groups in which every subgroup is subnormal of defect at most 3. Let G be a group which is either torsion-free or of prime exponent different from 7. We show that every subgroup in G is subnormal of defect at most 3 if and only if G is nilpotent of class at most 3. When G is of exponent 7 the situation is different. While every group of exponent 7, in which every subgroup is subnormal of defect at most 3, is nilpotent of class at most 4, there are examples of such groups with class exactly 4. We also investigate the structure of these groups.

MSC classification

Secondary: 20F19: Generalizations of solvable and nilpotent groups 20F45: Engel conditions 20F18: Nilpotent groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 3 , June 1998 , pp. 397 - 420
Copyright
Copyright © Australian Mathematical Society 1998

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