Normal Subgroups in Free Burnside Groups of Odd Period

Abstract

In the current paper we announce a positive answer for all prime numbers $n > 997$ to the following problem set by Adian in Kourovka Notebook: Is it true that all proper normal subgroups of the group $B(m, n)$ of prime period $n > 665$ are not free periodic groups? The current result also strengthens a similar result of Olshanskiy for sufficiently large odd numbers $n$ ($n > 10^{77}$).