A Simple Bound on the ℓ-Rank of Finite Gyrogroups
DOI:
https://doi.org/10.29020/nybg.ejpam.v19i2.7399Keywords:
generating set, gyrogroup, maximum order, rank, gyro-invariant setAbstract
In this article, we modify the definitions of left and right generating sets for a gyro-group, a group-like structure whose binary operation is generally non-associative. We then establish an upper bound for the minimal number of left generators of a finite gyrogroup, called the ℓ-rank of G, in terms of its order and the orders of its elements. This leads to the Maximum-Element-Order Problem for gyrogroups: given a finite gyrogroup G$, determine the maximum order of elements in G.
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Copyright (c) 2026 Teerapong Suksumran
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