On shift dynamics for cyclically presented groups

JOURNAL OF ALGEBRA

卷:418

Article

Bogley, William A.

关键词: Cyclically presented group;    Shift;    Fixed point free;    Asphericity;   

DOI  :  10.1016/j.jalgebra.2014.07.009

来源: Elsevier

【 摘 要 】

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. (c) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free