Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 28, No. 2, pp. 95-102 (2012)

On completely simple semigroups

F. Fatehi and M. R. Molaei

Shahid Bahonar University of Kerman

Abstract: In this paper completely simple semigroups or generalized groups are considered. We characterize generalized groups which are normal generalized groups. Homomorphisms of generalized groups are considered. Equivalent conditions for the kernel of a homomorphism are deduced. We prove that the group components of a generalized group have the same cardinality. We also prove that if $G$ is a finite normal generalized group, and $q| |G|$, where $q$ is a prime number, then $G$ has a generalized subgroup of order $q$. We deduce a theorem such as second isomorphism theorem for generalized groups.

Keywords: Completely simple semigroups, Normal generalized groups, Isomorphism theorem

Classification (MSC2000): 20M1; 20M99

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