  In universal algebraic geometry the category of the finite generated free
algebras of some fixed variety of algebras and the quotient group A/Y are very
important. Here A is a group of all automorphisms of this category and Y is a
group of all inner automorphisms of this category. In the varieties of all the
groups, all the abelian groups (see B. Plotkin and G. Zhitomirski, 2006), all
the nilpotent groups of the class no more then n (see A. Tsurkov, 2007) the
group A/Y is trivial. B. Plotkin posed a question: "Is there a subvariety of
the variety of all the groups, such that the group A/Y in this subvariety is
not trivial?" A. Tsurkov hypothesized that exist some varieties of periodic
groups, such that the groups A/Y in these varieties is not trivial. In this
paper we give an example of one subvariety of this kind.
