Effects of semigroup properties on local embeddability
Group Theory
2025-10-27 v1
Abstract
We investigate whether semigroups with a given property which are also locally embeddable into finite semigroups can be locally embedded into finite semigroups with the same property, obtaining a positive answer for completely simple and Clifford semigroups (similarly to group and inverse semigroup cases studied previously) and a negative answer for -trivial semigroups (similarly to cancellative semigroups). Additionally, we resolve the standing question on the differences between local embeddability in and local wrappability by finite structures, providing a novel construction of -trivial semigroups which satisfy the latter, but not the former.
Cite
@article{arxiv.2510.21349,
title = {Effects of semigroup properties on local embeddability},
author = {Dmitry Kudryavtsev},
journal= {arXiv preprint arXiv:2510.21349},
year = {2025}
}