3 papers
math.GR2017
On the semigroup rank of a group
Mário J. J. Branco, Gracinda M. S. Gomes, Pedro V. Silva
For an arbitrary group , it is shown that either the semigroup rank equals the group rank , or . This is the starting point f…
math.GR2016
Congruences on Direct Products of Transformation and Matrix Monoids
João Araújo, Wolfram Bentz, Gracinda Gomes
Malcev described the congruences of the monoid of all full transformations on a finite set . Since then, congruences have been characterized in various ot…
math.GR2015
Takahasi semigroups
Mário J. J. Branco, Gracinda M. S. Gomes, Pedro V. Silva
Takahasi's theorem on chains of subgroups of bounded rank in a free group is generalized to several classes of semigroups. As an application, it is proved that the subsemigroups of…