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Finite coverings by 2-engel groups

Published online by Cambridge University Press:  17 April 2009

Luise-Charlotte Kappe
Luise-Charlotte Kappe
Affiliation:
Department of Mathematical Sciences, University Center at Binghamton State University of New York, Binghamton, N.Y. 13901, United States of America
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Abstract

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Bear's characterisation of central-by-finite groups as groups possessing a finite covering by abelian subgroups if the starting point for this invertigation. We characterise groups with a finite covering by 2-Engel subgroups as groups for which the subgroup of right 2-Engel elements has finite index; and the groups having a finite covering by normal 2-Engel subgroups are exactly the 3-Engel groups among those having a finite covering by 2-Engel subgroups. The second centre of a group having a finite covering by class two subgroups does not necessarily have finite index. However, a group has a finite covering by subgroups in a variety containing all cyclic groups if the margin of thes variety in the group has finite index.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 1 , August 1988 , pp. 141 - 150
Copyright
Copyright © Australian Mathematical Society 1988

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