Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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53 citations
TL;DR: In this paper, it was shown that every group is a maximal subgroup of some free regular idempotent generated semigroup arising from a finite regular semigroup, and that every finite group is also a maximal group of such a semigroup.
Abstract: We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free regular idempotent generated semigroup arising from a finite regular semigroup. As a technical prerequisite for these results we establish a general presentation for the maximal subgroups based on a Reidemeister-Schreier type rewriting.
52 citations
51 citations
TL;DR: In this article, a semigroup F E that plays for a class of E -semi-adequate semigroups is presented, where F E is an inverse semigroup with semilattice of idempotents.
50 citations
TL;DR: In this article, it was shown that the category of right cancellative monoids and permissible homomorphisms is naturally equivalent to a category of O-simple inverse semigroups.
50 citations