On semilattices of groups whose arrows are epimorphisms

M. El-Ghali M. Abdallah, L. N. Gab-Alla and Sayed K. M. Elagan

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-26

Abstract:

A q partial group is defined to be a partial group, that is, astrong semilattice of groups S = [ E ( S ) ; S e , ϕ e , f ] such that S has an identity 1 and ϕ 1 , e is an epimorphism for all e ∈ E ( S ) . Every partial group S with identity contains a unique maximal q partial group Q ( S ) such that ( Q ( S ) ) 1 = S 1 . This Q operation is proved to commute with Cartesian products and preserve normality. With Q extended to idempotent separating congruences on S , it is proved that Q ( ρ K ) = ρ Q ( K ) for every normal K in S . Proper q partial groups are defined in such a way that associated to any group G , there is a proper q partial group P ( G ) with ( P ( G ) ) 1 = G . It is proved that a q partial group S is proper if and only if S ≅ P ( S 1 ) and hence that if S is any partial group, there exists a group M such that S is embedded in P ( M ) . P epimorphisms of proper q partial groups aredefined with which the category of proper q partial groups isproved to be equivalent to the category of groups and epimorphismsof groups.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:030673

DOI: 10.1155/IJMMS/2006/30673

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