Topic
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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3 citations
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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
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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
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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