On the semigroup rank of a group

Mário J. J. Branco, Gracinda M. S. Gomes, Pedro V. Silva

For an arbitrary group $G$, it is shown that either the semigroup rank $G\mathrm{rk}S$ equals the group rank $G\mathrm{rk}G$, or $G\mathrm{rk}S=G\mathrm{rk}G+1$. This is the starting point f…