Normal cryptogroups with an associate subgroup

Normal Cryptogroups with an Associate Subgroup

Let S be a semigroup. For a, x ∈ S such that a = axa, we say that x is an associate of a. A subgroup G of S which contains exactly one associate of each element of S is called an associate subgroup of S. It induces a unary operation in an obvious way, and we speak of a unary semigroup satisfying three simple axioms. A normal cryptogroup S is a completely regular semigroup whose H -relation is a...

Unary Semigroups with an Associate Subgroup

Homomorphisms and Congruences of Medial Semigroups with an Associate Subgroup

Let S be the model of a semigroup with an associate subgroup whose identity is a medial idempotent constructed by Blyth and Martins considered as a unary semigroup. For another such semigroup T , we construct all unary homomorphisms of S into T in terms of their parameters. On S we construct all unary congruences again directly from its parameters. This construction leads to a characterization ...

Three Amalgams with Remarkable Normal Subgroup Structures

We construct three groups Λ1, Λ2, Λ3, which can all be decomposed as amalgamated products F9∗F81F9 and have very few normal subgroups of finite or infinite index. Concretely, Λ1 is a simple group, Λ2 is not simple but has no non-trivial normal subgroup of infinite index, and Λ3 is not simple but has no proper subgroup of finite index.

Solvable $L$-subgroup of an $L$-group

In this paper, we study the notion of solvable $L$-subgroup of an $L$-group and provide its level subset characterization and this justifies the suitability of this extension. Throughout this work, we have used normality of an $L$-subgroup of an $L$-group in the sense of Wu rather than Liu.