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On Direct Decomposition of Partial Groups (Clifford Semigroups) and Generalized Fitting's Lemma

M. El-Ghali Mohamed Abdallah, Marwa A. El-Lithy

Abstract


In this paper we give further study of the direct decomposition of operator partial groups,equivalently Clifford semigroups or semilattices of groups. We introduce the key notion of an E-- embedding endomorphism and the generalized normal endomorphism and projection and establish the important Fitting's lemma for operator partial groups. We introduce the generalized nilpotent and central endomorphisms and develop their relations in connection with normal E-embedding endomorphisms. We develop the aspects of normal E-embedding endomorphisms of indecomposable operator partial groups with the maximal and minimal conditions on normal subpartial groups.

Keywords


Ω-partial group; E-embedding endomorphism; direct decomposition; projection; Fitting's Lemma; nilpotent endomorphism; central endomorphism.

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References


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: A.M. Abd Allah and M.E.-G.M. Abdallah, Congruences on Clifford semigroups, Pure Math. Manuscript 7 (1988), 19-35.

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