Takahasi semigroups

摘要

Takahasi’s Theorem on chains of subgroups of bounded rank ina free group is generalized to several classes of semigroups. As anapplication, it is proved that the subsemigroups ofperiodic points are finitely generated and periodic orbits arebounded for arbitrary endomorphisms for various semigroups.Some of these results feature classes such as completelysimple semigroups, Clifford semigroups or monoids defined bybalanced one-relator presentations.