Peter Cameron's homepage

Welcome to my St Andrews homepage. Under construction This page is under construction (and probably always will be!)

I am a half-time Professor in the School of Mathematics and Statistics at the University of St Andrews, and an Emeritus Professor of Mathematics at Queen Mary, University of London.

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School of Mathematics and Statistics
University of St Andrews
North Haugh
St Andrews, Fife KY16 9SS
SCOTLAND
Tel.: +44 (0)1334 463769
Fax: +44 (0)1334 46 3748
Email: pjc20(at)st-arthurs(dot)ac(dot)uk
  [oops – wrong saint!]





Page revised 2 April 2015

A problem

A quasigroup is a finite set with a binary operation satisfying the cancellation laws; that is, one whose Cayley table is a Latin square. A loop is a quasigroup with an identity element. The multiplication group of a quasigroup or loop is the group generated by the left and right translations (which are permutations).

It is known that almost every quasigroup (that is, a proportion tending to 1 as n → ∞) has multiplication group the symmetric group.

Problem: Does the same statement hold for loops?

Old problems are kept here.