Fox derivatives: a unique connection between group presentations and the integral group ring
Year: 2018
Type: article
Abstract: We give a criterion to determine whether generators can be removed from a finite presentation via Tietze transformations. We prove that for a generator in a pre- sentation ⟨X|R⟩ to be removable, there must exist a word in the normal closure of relators, R, whose Fox derivative is an invertible element in ZG. Furthermore, in this case all elements of ZG can be written as the derivative of words in R, with respect to the removable generator. We further discuss the application of this result on the theory units of group rings.
Author: Aryan Ghobadi
Institution: Queen Mary University of London
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3000557300