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Preprint Number 2120

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2120. Inessa I. Pavlyuk, Sergey V. Sudoplatov
Arities and aritizabilities of group, monoid and groupoid theories

Submission date: 21 December 2021


We study applications of a general approach for arities and arizabilities of theories to group and monoid theories. It is proved that a theory of a group G is aritizable if and only if G is finite. It is shown that this criterion does not hold for monoids/groupoids: there is an infinite monoid/groupoid having a binary theory.

Mathematics Subject Classification: 03C07, 03C10, 03C68, 20E34

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Full text arXiv 2112.11341: pdf, ps.

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