• ON SOME ASSOCIATE ALGEBRAIC STRUCTURES
Abstract
Nice loops are non-associative algebraic structures which lie between quasigroup and abelian group. In this paper, I prove some results on nice loops and uniform groups. Some algebraic structures with respect to newly defined binary operation called diamond are introduced in this paper. I also show that the collection of all oriented graphs forms a nice abelian loop and every additive group of order more than 3 forms 3-uniform, strong E-inversive and E-inversive E-nice abelian loop under the diamond operation.
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