English

Construction of Gyrogroups of Order $2^n$ by Cyclic 2-Groups

Group Theory 2023-03-03 v1

Abstract

A gyrogroup is a structure constituting from a non-empty set and a binary operation such that satisfying the left identity, and left inverse conditions, and also has the associative-like law said to be left gyroassociativity and left loop property. In this paper, we propose a method for constructing new gyrogroups of order 2n2^n by a cyclic 2-group that is Z2n\mathbb{Z}_{2^n}, where n3n\geq 3.

Keywords

Cite

@article{arxiv.2303.01066,
  title  = {Construction of Gyrogroups of Order $2^n$ by Cyclic 2-Groups},
  author = {Abraham A. Ungar and Mohammad Ali Salahshour and Kurosh Mavaddat Nezhaad},
  journal= {arXiv preprint arXiv:2303.01066},
  year   = {2023}
}