Splitting automorphisms of free Burnside groups

Abstract

It is proved that, if the order of a splitting automorphism of odd period of a free Burnside group is a prime, then the automorphism is inner. This implies, for every prime , an affirmative answer to the question on the coincidence of the splitting automorphisms of period of the group with the inner automorphisms (this question was posed in the “Kourovka Notebook” in 1990).Bibliography: 17 titles.