A Class Of Moufang Loops
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Date
1997-06
Authors
JAMAL, ENA
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Abstract
It is known that groups and Moufang loops are closely related. All groups are Moufang
loops but the converse is not true. It is, therefore, the aim of this research to determine
which Moufang loops are groups.
Let L be a Moufang loop of order n. For n = 2p2, where p is an odd prime, it can be
shown that L = C2 Xl C 2 or C2 ><l (Cp x Cp ) if L is not a cyclic group. Then it
p
was proved in [7] that L is a group in each case. This thesis studies Moufang loops of
the form L == Cs' Xl (Cpu X Cqll ), where s, p and q are primes. We prove that L is
a group for the following cases:
(a) p;t. q;
(b) P = q; and
( i ) s = 2 and p is odd; or
( ii) s = 2, P = 2 and ex = ~ = 1
( counter examples exist when ex or ~ is greater than 1 ); or
( iii) s is odd and p = 2.
Note: This problem is still open for the case p = q with sand p odd.
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A Class Of Moufang Loops