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Some finite groups with few defining relations

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

B. H. Neumann
B. H. Neumann
Affiliation:
Department of Mathematics Institute of Advanced Studies Australian National UniversityCanberra, ACT 2601 Australia Division of Mathematic and Statistics Commonwealth Scientific and Industrial Research Organization Canberra, ACT 2601, Australia
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Abstract

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Some new classes of finite groups with zero deficiency presentations, that is to say presentations with as few defining relations as generators, are exhibited. The presentations require 3 generators and 3 defining relations; the groups so presented can also be generated by 2 of their elements, but it is not known whether they can be defined by 2 relations in these generators, and it is conjectured that in general they can not. The groups themselves are direct products or central products of binary polyhedral groups with cyclic groups, the order of the cyclic factor being arbitrary.

MSC classification

Secondary: 20F05: Generators, relations, and presentations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 2 , April 1985 , pp. 230 - 240
Copyright
Copyright © Australian Mathematical Society 1985

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