## Loops and semidirect products (2000)

by
Michael K. Kinyon
,
Oliver Jones

Citations: | 7 - 4 self |

### BibTeX

@MISC{Kinyon00loopsand,

author = {Michael K. Kinyon and Oliver Jones},

title = {Loops and semidirect products},

year = {2000}

}

### OpenURL

### Abstract

A left loop (B, ·) is a set B together with a binary operation · such that (i) for each a ∈ B, the left translation mapping La: B → B defined by La(x) = a · x is a bijection, and (ii) there exists a two-sided identity 1 ∈ B satisfying 1 · x = x · 1 = x for every x ∈ B. A right loop is similarly defined, and a loop is both a right loop