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

Automorphisms of the category of finitely generated free groups of the some subvariety of the variety of all groups