Word equations in some geometric semigroups

The Word Problem for Semigroups 1 Semigroup Equations

is not always true for square integer matricesM and N . The most basic example of a semigroup is the set, Σ∗, of strings over an alphabet, Σ, where the binary operation is concatenation. In fact, we take the associativity of concatenation so much for granted that we typically write xyz for the concatenation of x, y, z ∈ Σ∗, without bothering to indicate whether they were concatenated as (x ◦ y)...

Equations in Finite Semigroups

We study the number of solutions of the general semigroup equation in one variable, X α = X β , as well as of the system of equations X 2 = X, Y 2 = Y, XY = Y X in H ≀ T n , the wreath product of an arbitrary finite group H with the full transformation semigroup T n on n letters. For these solution numbers, we provide explicit exact formulae, as well as asymptotic estimates. Our results concern...

Word Hyperbolic Semigroups 32

2 Word Hyperbolic Semigroups

The study of automatic and word hyperbolic groups is a prominent topic in geometric group theory. The definition of automatic groups extends naturally to semigroups [3, 8], but word hyperbolic groups are defined by a geometric condition, the thin triangle condition, whose extension is not immediate. The problem is that for semigroups the metric properties of the Cayley diagram are not as closel...

Some Results on Semigroups

In this note we state some results concerning the perturbation problem of strongly continuous semigroups on a Banach space X and provide some new characterizations of the uniformly continuous semigroups on X.