On Shift Dynamics for Cyclically Presented Groups

Citeable URL: https://ir.library.oregonstate.edu/concern/articles/c534fq74z

Descriptions

Attribute Name	Values
Creator	Bogley, William A.
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: Cyclically presented group, Asphericity, Fixed point free, Shift
Resource Type	Article
DOI	https://doi.org/10.1016/j.jalgebra.2014.07.009
Date Available	2015-01-06T20:20:13+00:00
Date Issued	2014-11-15
Citation	Bogley, W. A. (2014). On Shift Dynamics For Cyclically Presented Groups. Journal of Algebra, 418, 154-173. doi:10.1016/j.jalgebra.2014.07.009
Journal Title	Journal of Algebra
Journal Volume	418
Rights Statement	Copyright Not Evaluated
Publisher	Elsevier
Peer Reviewed	Yes
Language	English [eng]
Replaces	http://hdl.handle.net/1957/54833