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Abelian by cyclic groups resulting in Moufang loops

Abstract In 1999 Orin Chein and Andrew Rajah [Comment. Math. Univ. Carolin. 41: 237–244, 2000] presented the following question. If a Moufang loop G contains a normal abelian subgroup N of odd order such that G/N is cyclic, must G be a group? Here we prove that a Moufang loop that is an extension of an abelian group of odd order by a cyclic group has a normal subgroup of index dividing 3.