TITLE:
A Minimal Presentation of a Two-Generator Permutation Group on the Set of Integers
AUTHORS:
Simon Aloff, Michael Miniere, John T. Saccoman
KEYWORDS:
Permutation Groups, Combinatorial Group Theory, Presentation of Groups
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.11 No.10,
October
29,
2021
ABSTRACT: In this paper, we investigate the algebraic structure of certain 2-generator groups of permutations of the integers. The groups fall into two infinite classes: one class terminates with the quaternion group and the other class terminates with the Klein-four group. We show that all the groups are finitely presented and we determine minimal presentations in each case. Finally, we determine the order of each group.