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...

Among the most important and intensively studied classes of semigroups are finite semigroups, regular semigroups and inverse semigroups. Finite semigroups arise as syntactic semigroups of regular languages and as transition semigroups of finite automata. This connection has lead to a large and deep literature on classifying regular languages by means of algebraic properties of their correspondi...

We consider the question of membership of A ∨ G, where A and G are the pseudovarieties of finite aperiodic semigroups, and finite groups, respectively. We find a straightforward criterion for a semigroup S lying in a class of finite semigroups that are weakly abundant, to be in A ∨ G. The class of weakly abundant semigroups contains the class of regular semigroups, but is much more extensive; w...

A classification scheme for regular languages or finite semigroups was proposed by Pin through tree hierarchies, a scheme related to the concatenation product, an operation on languages, and to the Schützenberger product, an operation on semigroups. Starting with a variety of finite semigroups (or pseudovariety of semigroups) V, a pseudovariety of semigroups ◊u(V) is associated to each tree u. ...

We discuss the approximability of locally compact groups by finite semigroups and finite quasigroups (latin squares). We show that if a locally compact group G is approximable by finite semigroups, then it is approximable by finite groups, and thus many important groups are not approximable by finite semigroups. This result implies, in particular, the impossibility to simulate the field of real...

We consider certain abundant semigroups in which the idempotents form a subsemigroup, and which we call bountiful semigroups. We find a simple criterion for a finite bountiful semigroup to be a member of the join of the pseudovarieties of finite groups and finite aperiodic semigroups.

In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compac...

Herein we generalize the holonomy theorem for finite semigroups (see [7]) to arbitrary semigroups, S, by embedding s^ into an infinite Zeiger wreath product, which is then expanded to an infinite iterative matrix semigroup. If S is not finite-J-above (where finite-J-above means every element has only a finite number of divisors), then S is replaced by g3, the triple Schtitzenberger product, whi...

The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, Complexity of finite semigroups, Annals of Mathematics (2) 88 (1968), 128–160, motivated by the Prime Decomposition Theorem of K. Krohn and J. Rhodes, Algebraic theory of machines, I: Prime decomposition theorem for finite semigroups and machines, Transactions of the Ameri...