James E East

Aug 28, 2024 | fis.tu-dresden.de | James E East |Western Sydney |Victoria Gould |Craig Miller

For a semigroup (Formula presented.) whose universal right congruence is finitely generated (or, equivalently, a semigroup satisfying the homological finiteness property of being type right- (Formula presented.)), the right diameter of (Formula presented.) is a parameter that expresses how ‘far apart’ elements of (Formula presented.) can be from each other, in a certain sense.

Aug 28, 2024 | fis.tu-dresden.de | Peter Cameron |James E East |Western Sydney |Des Fitzgerald

For a positive integer n, the full transformation semigroup Tn consists of all self maps of the set {1, …, n} under composition. Any finite semigroup S embeds in some Tn, and the least such n is called the (minimum transformation) degree of S and denoted µ(S). We find degrees for various classes of finite semigroups, including rectangular bands, rectangular groups and null semigroups. The formulae we give involve natural parameters associated to integer compositions.