On the inner automorphisms of finite transformation semigroups

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

n-INNER AUTOMORPHISMS OF FINITE GROUPS

We refer to an automorphism g of a group G as n-inner if given any subset S of G with cardinality less than n, there exists an inner automorphism of G agreeing with g on S. Hence g is 2-inner if it sends every element of G to a conjugate. New examples are given of outer n-inner automorphisms of finite groups for all natural numbers n ≥ 2.

The Ranks of Some Transformation Semigroups on a Finite Set

UNIVERSAL COMPACTIFICATIONS OF TRANSFORMATION SEMIGROUPS

We extend the notion of semigroup compactification to the class of transformation semigroups, and determine the compactifications which are universal with respect to some topological properties.

On the Graphs Related to Green Relations of Finite Semigroups

In this paper we develop an analog of the notion of the con- jugacy graph of  nite groups for the  nite semigroups by considering the Green relations of a  nite semigroup. More precisely, by de ning the new graphs $Gamma_{L}(S)$, $Gamma_{H}(S)$, $Gamma_{J}(S)$ and $Gamma_{D}(S)$ (we name them the Green graphs) related to the Green relations L R J H and D of a  nite semigroup S , we  first atte...