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A Minimal Presentation of a Two-Generator Permutation Group on the Set of Integers
Middlesex College, Edison, NJ, USA
Middlesex College, Edison, NJ, USA
Seton Hall University, South Orange, NJ, USA
- 1 Middlesex College, Edison, NJ, USA
- 2 Middlesex College, Edison, NJ, USA
- 3 Seton Hall University, South Orange, NJ, USA
Advances in Pure Mathematics·Volume 11 (2021)·Pages 816–834·Published 13 October 2021·DOI10.4236/apm.2021.1110055
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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.
KeywordsPermutation GroupsCombinatorial Group TheoryPresentation of Groups
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