Every finite semigroup is embeddable in a finite relatively free semigroup
نویسنده
چکیده
The title result is proved by a Murskii-type embedding. Results on some related questions are also obtained. For instance, it is shown that every finitely generated semigroup satisfying an identity ξ d = ξ2d is embeddable in a relatively free semigroup satisfying such an identity, generally with a larger d ; but that an uncountable semigroup may satisfy such an identity without being embeddable in any relatively free semigroup. It follows from known results that every finite group is embeddable in a finite relatively free group. It is deduced from this and the proof of the title result that a finite monoid S is embeddable by a monoid homomorphism in a finite (or arbitrary) relatively free monoid if and only if its group of invertible elements is either {e} or all of S. MSC: Primary: 20M05; secondary: 20M07, 20M30.
منابع مشابه
Presentations for Subsemigroups of Groups
This thesis studies subsemigroups of groups from three perspectives: automatic structures, ordinary semigroup presentations, and Malcev presentaions. [A Malcev presentation is a presentation of a special type for a semigroup that can be embedded into a group. A group-embeddable semigroup is Malcev coherent if all of its finitely generated subsemigroups admit finite Malcev presentations.] The th...
متن کاملClassification of Monogenic Ternary Semigroups
The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...
متن کاملOn Maximal Subgroups of Free Idempotent Generated Semigroups
We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free...
متن کاملNormal Forms for Free Aperiodic Semigroups
The implicit operation ω is the unary operation which sends each element of a finite semigroup to the unique idempotent contained in the subsemigroup it generates. Using ω there is a well-defined algebra which is known as the free aperiodic semigroup. In this article we show that for each n, the ngenerated free aperiodic semigroup is defined by a finite list of pseudoidentities and has a decida...
متن کاملDerivations on Certain Semigroup Algebras
In the present paper we give a partially negative answer to a conjecture of Ghahramani, Runde and Willis. We also discuss the derivation problem for both foundation semigroup algebras and Clifford semigroup algebras. In particular, we prove that if S is a topological Clifford semigroup for which Es is finite, then H1(M(S),M(S))={0}.
متن کامل