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Bicyclic semigroup

About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.


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Journal ArticleDOI
TL;DR: In this article, it was shown that S (C ) contains a copy of the bifree locally inverse semigroup, if C is a group on X and S(C ) is a completely simple semigroup on X.

3 citations

Journal ArticleDOI
TL;DR: In this article, the authors show that the dihedral group may serve as the group G-normal for semigroups of transformations of X>>\s n>>\s, and characterize a large class of dihedral groups with G-normax membership.
Abstract: Given a subgroup G of the symmetric group S n on n letters, a semigroup S of transformations of X n is G-normal if G S =G, where G S consists of all permutations h∈S n such that h −1 fh∈S for all f∈S. A semigroup S is G-normax if it is a maximal semigroup in the set of all G-normal semigroups. In 1996, I. Levi showed that the alternating group A n can not serve as the group G S for any semigroup of total transformations of X n . In 2000 and 2001, I. Levi, D.B. McAlister and R.B. McFadden described all A n -normal semigroups of partial transformations of X n . Also, in 1994, I. Levi and R.B. McFadden described all S n -normal semigroups. In this paper, we show that the dihedral group D n may serve as the group G S for semigroups of transformations of X n . We characterize a large class of D n -normax semigroups and describe certain D n -normal semigroups.

3 citations

Journal ArticleDOI
TL;DR: In this article, a semigroup S is called a ∇-semigroup if the set of all its full sub-semigroups forms a chain under set inclusion, and several characterization theorems of such semigroups are established.
Abstract: A semigroup S is called a ∇-semigroup if the set of all its full subsemigroups forms a chain under set inclusion. In this paper, we investigate some properties of such kind of semigroups and establish several characterization theorems of type-A ∇-semigroups. Our theorems generalize the known results of P. R. Jones obtained in 1981 on inverse semigroups whose full inverse subsemigroups form a chain.

3 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202312
202229
20217
20203
20194
201810