Disassociativity in Conjugacy Closed Loops

Author(s)

• J.D. Phillips

Journal Title/Source

Communications in Algebra

Publication Date

2004

Volume

32

Page Numbers

767-786

Document Type

Journal Article

Department

Mathematics and Computer Science

Abstract

Let Q be a conjugacy closed loop, and N(Q) its nucleus. Then Z(N(Q)) contains all associators of elements of Q. If in addition Q is diassociative (i.e., an extra loop), then all these associators have order 2. If Q is power-associative and |Q| is finite and relatively prime to 6, ten Q is a group. If Q is a finite non-associative extra loop, then 16 | |Q|.

Recommended Citation

Phillips, J.D., "Disassociativity in Conjugacy Closed Loops" (2004). Journal Articles. 544.
https://commons.nmu.edu/facwork_journalarticles/544