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arXiv · 2509.11610

Beyond wreath and block

Michal Botur·Tomasz Kowalski
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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.

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Michal Botur, Tomasz Kowalski. 2025-09-15. Beyond wreath and block. https://doi.org/10.1007/s00233-022-10291-5

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