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ON GROUPS PRESENTED BY MONADIC REWRITING SYSTEMS WITH GENERATORS OF FINITE ORDER

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  06 March 2015

ADAM PIGGOTT
ADAM PIGGOTT*
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA email [email protected]
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Abstract

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We prove that the groups presented by finite convergent monadic rewriting systems with generators of finite order are exactly the free products of finitely many finite groups, thereby confirming Gilman’s conjecture in a special case. We also prove that the finite cyclic groups of order at least three are the only finite groups admitting a presentation by more than one finite convergent monadic rewriting system (up to relabelling), and these admit presentation by exactly two such rewriting systems.

Keywords

groupmonoid presentationrewriting systemmonadic systemplain group

MSC classification

Primary: 20F10: Word problems, other decision problems, connections with logic and automata
Secondary: 20E99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 3 , June 2015 , pp. 426 - 434
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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