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Preprint . 2018
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Journal of Algebra
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Gilman's conjecture

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2019Embargo end date: 01 Jan 2018 Australia English Publisher:Elsevier BVJournal:Journal of Algebra, volume 517, pages 167-185 (issn: 0021-8693, Copyright policy )
Authors: Eisenberg, Andy; Piggott, Adam;

doi: 10.1016/j.jalgebra.2018.09.022 , 10.48550/arxiv.1806.06155

arXiv: 1806.06155

Gilman's conjecture

Abstract

We prove a conjecture made by Gilman in 1984 that the groups presented by finite, monadic, confluent rewriting systems are precisely the free products of free and finite groups.

21 pages, 8 figures

Country
Australia
Related Organizations
Keywords

Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Generators, relations, and presentations of groups, Groups, groups, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), Group Theory (math.GR), free products with amalgamation, 20E06, 20F10, 68Q42, 20E08, and generalizations, Higman-Neumann-Neumann extensions, and generalizations, free products, Free products, Free products with amalgamation, Grammars and rewriting systems, FOS: Mathematics, Higman–Neumann–Neumann extensions, Foundations of computer science, Rewriting systems, Mathematics - Group Theory, 2602 Algebra and Number Theory, rewriting systems

  • BIP!
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    selected citations
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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 3
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
Green