The unique trace property of n-periodic product of groups

In this paper we prove the unique trace property of C *-algebras of n-periodic products of arbitrary family of groups without involutions. We show that the free Burnside groups B ( m , n ) and their automorphism groups also possess the unique trace property. Also, we show that every countable group is embedded into some 3-generated group with the unique trace property, while every countable periodic group of bounded period and without involutions is embedded into some 3- generated periodic group G of bounded period with the unique trace property. Moreover, as a group G can be chosen both simple and not simple group.