Universally noncommutative loops

Andries Brouwer, Ian Murray Wanless

Research output: Contribution to journalArticleResearchpeer-review


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 languageEnglish
Pages (from-to)113 - 115
Number of pages3
JournalBulletin of the Institute of Combinatorics and its Applications
Publication statusPublished - 2011

Cite this