Half-automorphism group of a class of Bol loops

Dylene Agda Souza de Barros; Giliard Souza dos Anjos

Half-automorphism group of a class of Bol loops

Group Theory 2022-02-08 v1

Authors: Dylene Agda Souza de Barros , Giliard Souza dos Anjos

Abstract

A Bol loop is a loop that satisfies the Bol identity $(xy.z)y=x(yz.y)$ . If $L$ is a loop and $f:L\to L$ is a bijection such that $f(xy)\in\{f(x)f(y),f(y)f(x)\}$ , for every $x$ , $y\in L$ , then $f$ is called a half-automorphism of $L$ . In this paper, we describe the half-automorphism group of a class of Bol loops of order $4m$ .

Keywords

bol loop half-automorphism loop theory bol identity finite loops

Cite

@article{arxiv.2202.03405,
  title  = {Half-automorphism group of a class of Bol loops},
  author = {Dylene Agda Souza de Barros and Giliard Souza dos Anjos},
  journal= {arXiv preprint arXiv:2202.03405},
  year   = {2022}
}

Comments

14 pages

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