On completely simple semigroups

Fatehi, F. and Molaei, M. R. (2012) On completely simple semigroups. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 28 (2). pp. 95-102. ISSN 0866-0174

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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.

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