## M. Hossein Shahzamanian's Annual Report

## Year:

## Brief description of the research activities:

The first section of my Postdoc proposal's plan is about tameness for pseudovarieties of groups, in which one of the interest problem is to investigate whether pseudovarieties like solvable groups, groups of odd order, and nilpotent groups are tame.

A pseudovariety of finite groups $\bf{G}_{nil}$ is not arborescent pseudovariety; I was interested to investigate whether the product of $nil$-closed finitely generated subgroups is $nil$-closed. It leads me to work on similar result like the results concern to the extension closed pseudovarieties of groups. I understood that Almeida and Steinberg provide an example of two $nil$-closed finitely generated subgroups of a free group whose product is not $nil$-closed. As they work had not finished, I had worked on it to extend the obtained result.

I finished the last paper out of my Ph.D. thesis during my Postdoc period at Porto but a large part of this work was done while I was working at Vrije Universiteit Brussel. In the case of finite groups a characterization of minimal non-nilpotent has been given by Schmidt. In this paper, we provide a characterization for $S$, a finite minimal non-nilpotent semigroup that $S$ is either a Schmidt group or a semigroup of type $U_1$, $U_2$, $U_3$, $U_4$ or $U_5$.