Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584643 | Journal of Algebra | 2014 | 20 Pages |
Abstract
A group defined by a finite presentation with cyclic symmetry admits a shift automorphism that is periodic and word-length preserving. It is shown that if the presentation is combinatorially aspherical and orientable, in the sense that no relator is a cyclic permutation of the inverse of any of its shifts, then the shift acts freely on the non-identity elements of the group presented. For cyclic presentations defined by positive words of length at most three, the shift defines a free action if and only if the presentation is combinatorially aspherical and the shift itself is fixed point free if and only if the group presented is infinite.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
William A. Bogley,