Diassociativity in Conjugacy Closed Loops

By Michael K. Kinyon, Kenneth Kunen, J. Phillips. 2002

57 citations recorded by the source corpus.

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, then Q is a group. If Q is a finite non-associative extra loop, then 16 ∣ |Q|.

Subfields: Electrical and Electronic Engineering, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/035b279c61e2acb234c07bbe3d2ab54bc560b043

How researchers see this paper

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In Electrical and Electronic Engineering

1. Michael K. Kinyon
2. Kenneth Kunen

In Geometry and Topology

1. Michael K. Kinyon
2. Kenneth Kunen

In Theoretical Computer Science

1. Michael K. Kinyon
2. Kenneth Kunen

Citations in the corpus

• The structure of extra loops (2004, methodology): “A start on such a theory was made in [20], where it was shown that if Q is a finite nonassociative extra loop, then |N | is even and |Q : N | ≥ 8, so that 16 | |Q|.”