2 research outputs found
Anisimov's Theorem for inverse semigroups
The idempotent problem of a finitely generated inverse semigroup is the
formal language of all words over the generators representing idempotent
elements. This note proves that a finitely generated inverse semigroup with
regular idempotent problem is necessarily finite. This answers a question of
Gilbert and Noonan Heale, and establishes a generalisation to inverse
semigroups of Anisimov's Theorem for groups.Comment: 8 page
Inverse semigroups with rational word problem are finite
This note proves a generalisation to inverse semigroups of Anisimov's theorem
that a group has regular word problem if and only if it is finite, answering a
question of Stuart Margolis. The notion of word problem used is the two-tape
word problem -- the set of all pairs of words over a generating set for the
semigroup which both represent the same element.Comment: 6 pages, no figure