Submission date: 21 December 2021

Abstract:

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

Keywords and phrases:

Full text arXiv 2112.11341: pdf, ps.