Bezverhnii

pp. 43-63

pp. 238-256

pp. 70-101

In this paper the author proves that in groups with small cancellation conditions C(3)-T(6) an occurrence problem in a cyclic subgroup is solvable; in other words, for any elements (g,h) of such a group one can determine whether there exists an integer n≠ ±1:gⁿ=h. This result is the latest in a series of theorems on groups with small cancellation conditions C(p)-T(q), proved by the author: on resolvability of a root problem, on resolvability of a problem of conjugated appearance in a cyclic subgroup, on the norm forms of elements in the infinite order and on the characteristic property of elements in the finite order. The results were obtained with the use of the group diagram method. As a direction for further development, it is planned to solve a problem of power conjugation in the specified class of groups.