On HNN-extensions in the class of groups of large odd exponent

A sufficient condition for the existence of HNN-extensions in the class of groups of odd exponent n much greater than 1 is given in the following form. Let Q be a group of odd exponent n > 2(48) and G be an HNN-extension of Q. If A is an element of G then let F(A) denote the maximal subgroup of Q which is normalized by A. By tau(A) denote the automorphism of F(A) which is induced by conjugation by A. Suppose that for every A is an element of G which is not conjugate to an element of Q the group <tau(A), F(A)> has exponent n and, in addition, equalities A(-k)q(0)A(k) = q(k), where q(k) is an element of Q and k = 0, 1,..., [2(-16)n] ([2(-16)n] is the integer part of 2(-16)n), imply that q(0) is an element of F(A). Then the group Q naturally embeds in the quotient G/G(n), that is, there exists an analogue of the HNN-extension 9 of Q in the class of groups of exponent n.