Topic
Bol loop
About: Bol loop is a research topic. Over the lifetime, 82 publications have been published within this topic receiving 958 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, it was shown that the gyrogroup [1] is just the well known left Bol loop with Bruck identity, and the other constructions of [2] are also discussed.
Abstract: It is shown that the gyrogroup [1] is just the well known left Bol loop with Bruck identity. This result has been announced in [12]. The other constructions of [1] are also discussed.
58 citations
TL;DR: In the spirit of Glauberman's fundamental work in B-loops and Moufang loops, this article proved Cauchy and strong Lagrange theorems for Bol loops of odd order.
Abstract: In the spirit of Glauberman’s fundamental work in B-loops and Moufang loops [18, 19], we prove Cauchy and strong Lagrange theorems for Bol loops of odd order We also establish necessary conditions for the existence of a simple Bol loop of odd order, conditions which should be useful in the development of a Feit-Thompson theorem for Bol loops Bol loops are closely related to Aschbacher’s twisted subgroups [1], and we survey the latter in some detail, especially with regard to the so-called Aschbacher radical
53 citations
TL;DR: In this article, Loops and semidirect products are discussed in the context of semidefinite linear algebra, and the authors propose Loops-and-Semidirect Products (Loops and Semi-Direct Products) algorithm.
Abstract: (2000). Loops and semidirect products. Communications in Algebra: Vol. 28, No. 9, pp. 4137-4164.
33 citations
1 May 1981
TL;DR: In this article, it was shown that for any odd prime p, a Moufang loop of order 2 p 2 is a group and there is exactly one non-associative right Bol loop.
Abstract: In this paper we prove that for any odd prime p , a Moufang loop of order 2 p 2 is a group and there is exactly one non-associative right Bol loop of order 2 p 2 .
27 citations
Posted Content•
TL;DR: In the spirit of Glauberman's fundamental work in B-loops and Moufang loops, this paper proved Cauchy and strong Lagrange theorems for Bol loops of odd order.
Abstract: In the spirit of Glauberman's fundamental work in B-loops and Moufang loops, we prove Cauchy and strong Lagrange theorems for Bol loops of odd order. We also establish necessary conditions for the existence of a simple Bol loop of odd order, conditions which should be useful in the development of a Feit-Thompson theorem for Bol loops. Bol loops are closely related to Aschbacher's twisted subgroups, and we survey the latter in some detail, especially with regard to the so-called Aschbacher radical.
25 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 1 |
| 2019 | 1 |
| 2018 | 2 |
| 2017 | 2 |
| 2016 | 1 |