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Elementary amenable groups of finite hirsch length are locally-finite by virtually-solvable

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

J. A. Hillman  and
P. A. Linnell
J. A. Hillman
Affiliation:
The University of SydneySydney NSW 2006, Australia
P. A. Linnell
Affiliation:
Virginia Polytechnic Institute and State UniversityBlacksburg, VA 24061-0123
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Abstract

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If G is an elementary amenable group of finite Hirsch length h, then the quotient of G by its maximal locally finite normal subgroup has a maximal solvable normal subgroup, of derived length and index bounded in terms of h.

Keywords

cohomological dimensionelementary amenablegroupHirsch lengthsolvable.

MSC classification

Secondary: 20F19: Generalizations of solvable and nilpotent groups 20F38: Other groups related to topology or analysis
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 52 , Issue 2 , April 1992 , pp. 237 - 241
Copyright
Copyright © Australian Mathematical Society 1992

References

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