×

zbMATH — the first resource for mathematics

On elements of \(T(6)\)-\(1/3\) groups. (Russian) Zbl 1113.20306
A finitely presented group \(G\) is called \(T(6)\)-\(1/3\) group if the symmetrized set \(R\) of all defining words of \(G\) satisfies the conditions \(C'(1/3)\) and \(T(6)\). Theorem 1. An element \(W\) from a \(T(6)\)-\(1/3\) group has finite order \(n\) if and only if there exists a defining word \(U^k\) and \(W\) is conjugate to \(U^j\) for \(k\) dividing \(jn\).
MSC:
20F06 Cancellation theory of groups; application of van Kampen diagrams
20F05 Generators, relations, and presentations of groups
PDF BibTeX XML Cite