Asian Journal of Pure and Applied Mathematics

Maximal Normal Subloops of Moufang Loop of Odd Order pα q4

Lois A. Ademola *

Department of Mathematics, University of Jos, Plateau state, Nigeria.

Naphtali B. Jelten

Department of Mathematics, University of Jos, Plateau state, Nigeria.

*Author to whom correspondence should be addressed.

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Abstract

Let L be a Moufang loop of order p^\(\alpha\) q⁴   where p and q are primes with 3< p <q, q \(\not\equiv\) 1 (mod p)  and \(\alpha\) \(\in\) {1,2,3,4}. In this paper, with the extra condition that L_a  = q²  and  L_a \(\subset\) N, we obtain the chain of all possible maximal normal subloop M  of L.

Keywords: Colchiploidy, Moufang loop, Breeding Vigna, order, prime, nonassociative, maximal normal, subloops

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