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

Adam Piggott

doi:10.1017/S0004972715000015

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

Adam Piggott^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	426-434
Number of pages	9
Journal	Bulletin of the Australian Mathematical Society
Volume	91
Issue number	3
DOIs	https://doi.org/10.1017/S0004972715000015
Publication status	Published - 24 Apr 2015
Externally published	Yes

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abstract = "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.",

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AB - 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.

KW - group

KW - monadic system

KW - monoid presentation

KW - plain group

KW - rewriting system

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DO - 10.1017/S0004972715000015

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IS - 3

ER -

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

Abstract

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