CERTAIN CYCLICALLY PRESENTED GROUPS ARE INFINITE

Abstract

We prove that the groups in two infinite families considered by Johnson, Kim and O'Brien are almost all infinite.

ACKNOWLEDGMENTS

This work was undertaken while all three authors were at the Mathematics Institute to take part in the Warwick Workshop on Computation in Group Theory and Geometry, 9–17 July 1999, supported by the University of Warwick. We are grateful to fellow participant Martin Edjvet who encouraged us to consider the question. The first author was partially supported by the Australian Research Council and the third author was partially supported by an ESPRC grant.