Finite coverings by 2-engel groups

Author:

Kappe Luise-Charlotte

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference11 articles.

1. On the Engel margin

2. Varieties of Groups

3. Verbal and Marginal Subgroups;Hall;J. Reine Angew. Math.,1940

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1. Finite coverings: A journey through groups, loops, rings and semigroups;Group Theory, Combinatorics, and Computing;2014

2. How Abelian is a Finite Group?;The Mathematics of Paul Erdős I;2013

3. On non abelian tensor analogues of 3-Engel groups;Indagationes Mathematicae;2012-09

4. On loops covered by subloops;Expositiones Mathematicae;2005-09

5. ON NONABELIAN TENSOR ANALOGUES OF 2-ENGEL CONDITIONS;Glasgow Mathematical Journal;2005-02

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