[2402.00417] Presentation of monoids generated by a projection and an involution
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Mathematics > Group Theory

arXiv:2402.00417 (math)
[Submitted on 1 Feb 2024]

Title:Presentation of monoids generated by a projection and an involution

Authors:Pascal Caron, Jean-Gabriel Luque, Bruno Patrou
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Abstract:Monoids generated by elements of order two appear in numerous places in the literature. For example, Coxeter reflection groups in geometry, Kuratowski monoids in topology, various monoids generated by regular operations in language theory and so on. In order to initiate a classification of these monoids, we are interested in the subproblem of monoids, called strict 2-PIMs, generated by an involution and an idempotent. In this case we show, when the monoid is finite, that it is generated by a single equation (in addition to the two defining the involution and the idempotent). We then describe the exact possible forms of this equation and classify them. We recover Kuratowski's theorem as a special case of our study.
Subjects: Group Theory (math.GR); Formal Languages and Automata Theory (cs.FL)
Cite as: arXiv:2402.00417 [math.GR]
  (or arXiv:2402.00417v1 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.2402.00417

Submission history

From: Pascal Caron [view email]
[v1] Thu, 1 Feb 2024 08:34:39 UTC (26 KB)
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