Universally noncommutative loops

Andries Brouwer; Ian Murray Wanless

Universally noncommutative loops

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

We call a loop universally noncommutative if it does not have a loop isotope in which two non-identity elements commute. Finite universally noncommutative loops are equivalent to latin squares that avoid the configuration: (., alpha, beta; alpha, ., gamma; beta, gamma, .) (fig.1) By computer enumeration we find that there are only two species of universally non commutative loops of order =<11. Both have order 8

Original language	English
Pages (from-to)	113 - 115
Number of pages	3
Journal	Bulletin of the Institute of Combinatorics and its Applications
Volume	61
Publication status	Published - 2011

Cite this

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title = "Universally noncommutative loops",

abstract = "We call a loop universally noncommutative if it does not have a loop isotope in which two non-identity elements commute. Finite universally noncommutative loops are equivalent to latin squares that avoid the configuration: (., alpha, beta; alpha, ., gamma; beta, gamma, .) (fig.1) By computer enumeration we find that there are only two species of universally non commutative loops of order =<11. Both have order 8",

author = "Andries Brouwer and Wanless, \{Ian Murray\}",

year = "2011",

language = "English",

volume = "61",

pages = "113 -- 115",

journal = "Bulletin of the Institute of Combinatorics and its Applications",

issn = "1183-1278",

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T1 - Universally noncommutative loops

AU - Brouwer, Andries

AU - Wanless, Ian Murray

PY - 2011

Y1 - 2011

N2 - We call a loop universally noncommutative if it does not have a loop isotope in which two non-identity elements commute. Finite universally noncommutative loops are equivalent to latin squares that avoid the configuration: (., alpha, beta; alpha, ., gamma; beta, gamma, .) (fig.1) By computer enumeration we find that there are only two species of universally non commutative loops of order =<11. Both have order 8

AB - We call a loop universally noncommutative if it does not have a loop isotope in which two non-identity elements commute. Finite universally noncommutative loops are equivalent to latin squares that avoid the configuration: (., alpha, beta; alpha, ., gamma; beta, gamma, .) (fig.1) By computer enumeration we find that there are only two species of universally non commutative loops of order =<11. Both have order 8

M3 - Article

SN - 1183-1278

VL - 61

SP - 113

EP - 115

JO - Bulletin of the Institute of Combinatorics and its Applications

JF - Bulletin of the Institute of Combinatorics and its Applications

ER -