Volume 37 • Number 2 • 2014   • Moufang Loops of Odd Order $pq^4$ Wing Loon Chee and Andrew Rajah Abstract. The paper continues on the characterisation of positive integers n for which all Moufang loops of order n are associative. We study the case $n = pq^4$ where p and q are distinct odd primes, and show that all Moufang loops of order $pq^4$ are associative if and only if $q ≠ 3$ and $q ≠ 1$ (mod p). 2010 Mathematics Subject Classification: 20N05 Full text: PDF