| Popis: |
In this paper we investigate the structure of the ring diagrams with periodic marks in groups with small cancellation conditions C (3) T (6). These diagrams are used to solve the tasks such as the problem of conjugate words, the problem of conjugate occurrence in cyclic subgroup, and the problem of power conjugacy. In groups of this class the first two problems are solved positively. The third is formulated as follows: to find out if there are integers of m, n, for which the degree of words v, w with indicators of m, n are respectively conjugated in the group G = (X; R).To solve this problem it is sufficient to obtain upper bounds for the lengths of boundary marks of a conjugacy diagram, or to limit the modules of the integers n, m. This is the subject of this paper.Exploring the diagrams of conjugacy of words degrees, irreducible in a special sense, it becomes possible to break a set of these diagrams into three classes. Working with one of these classes, and using the periodicity of boundary marks of a diagram it becomes possible to prove the periodicity of the layers in this diagram, and later on also to limit the length of the borders. In another class is a sufficient to limit the lengths of the boundary marks since the diagrams in this class are not the n-layered, and their boundary marks intersect.Thus, it becomes possible to limit the degree indicators of the conjugate words thereby, in fact, solving the formulated problem in the considered class of groups, provided that the diagram of conjugacy belongs to the second class mentioned. Hence, the final solution of the power conjugacy problem requires its solving for the case of diagrams of the third type. |
