Title

On Groups Presented by Monadic Rewriting Systems with Generators of Finite Order

Publication Date

2015

Journal

Bulletin of the Australian Mathematical Society

Volume

91

Issue

3

First Page

426

Last Page

434

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 relabeling), and these admit presentation by exactly two such rewriting systems.

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