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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

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Volume 15, Issue 6


Presentations for rigid solvable groups

Nikolay S. Romanovskiy
Published Online: 2012-11-01 | DOI: https://doi.org/10.1515/jgt-2012-0025


A group G is said to be m-rigid if it has a normal series

in which each factor is abelian and torsion-free as a -module. Denote by the class of all m-rigid groups and by the set of groups in generated by that satisfy a given set of relations R. We say that a group in is maximal if it has no proper covering in . It is proved that, for every R, the set contains only finitely many maximal groups. The set of relations R is said to be complete if contains a unique maximal group. It is shown that every finitely generated group in is completely finitely presented. We give a definition of a canonical presentation for a rigid group with the generators . If such a presentation is given, the group at least has decidable word problem. Given a finite set of relations , we effectively construct a finite set of canonical presentations in the generators for groups in among which all the maximal groups in are contained.

About the article

Received: 2012-02-05

Published Online: 2012-11-01

Published in Print: 2012-11-01

Citation Information: Journal of Group Theory, Volume 15, Issue 6, Pages 793–810, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt-2012-0025.

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