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On stallings' unique factorisation groups

Published online by Cambridge University Press:  17 April 2009

Donald I. Cartwright  and
Bernhard Krön
Donald I. Cartwright
Affiliation:
School of Mathematics and Statistics, The University of Sydney, New South Wales 2006, Australia, e-mail: [email protected], [email protected]
Bernhard Krön
Affiliation:
School of Mathematics and Statistics, The University of Sydney, New South Wales 2006, Australia, e-mail: [email protected], [email protected]
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Let Γ be a group and Σ a symmetric generating set for Γ. In 1966, Stallings called Γ a unique factorisation group if each group element may be written in a unique way as a product a1…am, where ai ∈ Σ for each i and aiai+1 ∉ Σ ∪ {1} for each i < m. In this paper we give a complete combinatorial proof of a theorem, not explicitly stated by Stallings in 1966, characterising all such pairs (Γ, Σ). We also characterise the unique factorisation pairs by a certain tree-like property of their Cayley graphs.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 1 , February 2006 , pp. 27 - 36
Copyright
Copyright © Australian Mathematical Society 2006

References

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