Beyond wreath and block
Group Theory
2025-09-16 v1
Abstract
We investigate a semigroup construction generalising the two-sided wreath product. We develop the foundations of this construction and show that for groups it is isomorphic to the usual wreath product. We also show that it gives a slightly finer version of the decomposition in the Krohn-Rhodes Theorem, in which the three-element flip-flop monoid is replaced by the two-element semilattice.
Keywords
Cite
@article{arxiv.2509.11610,
title = {Beyond wreath and block},
author = {Michal Botur and Tomasz Kowalski},
journal= {arXiv preprint arXiv:2509.11610},
year = {2025}
}