Loops and Semidirect Products
Oliver Jones, Michael K. Kinyon
Abstract
A loop (B,·) is a set B together with a binary operation · such that (i) for each a∈ B, the left and right translation mappings La:B B: x a· x and Ra:B B: x x· a are bijections, and (ii) there exists a two-sided identity element 1∈ B. Thus loops can be thought of as "nonassociative groups". In this paper we study standard, internal and external semidirect products of loops with groups. These are generalizations of the familiar semidirect product of groups.
Create a lesson
Related papers
Property R∞ for Artin and Coxeter groups whose outer automorphisms are length-preserving
Ignat Soroko
DL, DQ Spectrum and Eigenvalue-free Interval of Cayley Graphs over Finite Nilpotent Groups
Pallabi Manna, Santanu Mandal
On p-groups with one nonlinear codegree
Jiwei Zheng, Heng Lv
Classes of Subgroups of a finite group with isomorphic quotient groups
Tushar Halder, Sachin Ballal
Cohomology and multiplicative gaps for quasi-isometries of nilpotent groups
Mayukh Mukherjee, Soumyadeb Samanta, Soumyadip Thandar
On the number of conjugacy classes of finite solvable groups of order divisible by p2
Thomas Michael Keller