Generalized Groups

(Khaled Ahmed Ali Aldwoah)

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Abstract

The aim of this paper is to generalize the concept of a group where the triple (G, E, ⋆) represents a generalized group if G is a nonempty set, E represents an equivalence relation defined on G and the operation ⋆ is a function of G×G satisfying some conditions. The paper also reveals some concepts and provides some examples related to generalized groups.

KEYWORDS
Generalized subgroup, generalized semigroup, equivalence relation

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References

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