Welcome to my St Andrews homepage. This page is under construction (and probably always will be!)
I am a halftime 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.
Events
About me
On this site

Elsewhere

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)starthurs(dot)ac(dot)uk [oops – wrong saint!] 
Page revised 2 April 2015 
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.