A note on maximal subgroups of free idempotent generated semigroups over bands
Igor Dolinka
TL;DR
This paper characterizes when all maximal subgroups of free idempotent generated semigroups over bands are free, showing it occurs precisely for bands in certain seminormal varieties.
Contribution
It provides a complete characterization of band varieties where all maximal subgroups are free, focusing on left and right seminormal bands.
Findings
Maximal subgroups are free if and only if the band belongs to a seminormal variety.
The result applies to all bands within the specified varieties.
The paper advances understanding of the structure of free idempotent generated semigroups.
Abstract
We prove that all maximal subgroups of the free idempotent generated semigroup over a band B are free for all B belonging to a band variety V if and only if V consists either of left seminormal bands, or of right seminormal bands.
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