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Minimal generating sets for some wreath products of groups

Published online by Cambridge University Press:  17 April 2009

Yeo Kok Chye
Yeo Kok Chye
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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Let d(G) denote the minimum of the cardinalities of the generating sets of the group G. Call a generating set of cardinality d(G) a minimal generating set for G. If A is a finitely generated nilpotent group, B a non-trivial finitely generated abelian group and A wr B is their (restricted, standard) wreath product, then it is proved (by explicitly constructing a minimal generating set for A wr B ) that d(AwrB) = max{l+d(A), d(A×B)} where A × B is their direct product.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 1 , August 1973 , pp. 127 - 136
Copyright
Copyright © Australian Mathematical Society 1973

References

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