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arXiv · 2303.01066

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

Abraham A. Ungar·Mohammad Ali Salahshour·Kurosh Mavaddat Nezhaad
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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 $2^n$ by a cyclic 2-group that is $\mathbb{Z}_{2^n}$, where $n\geq 3$.

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Abraham A. Ungar, Mohammad Ali Salahshour, Kurosh Mavaddat Nezhaad. 2023-03-02. Construction of Gyrogroups of Order $2^n$ by Cyclic 2-Groups. https://arxiv.org/abs/2303.01066

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