The commutative Moufang loops with minimum conditions for subloops~II

N. I. Sandu

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2004), pp. 33-48

Résumé

It is proved that the following conditions are equivalent for an infinite nonassociative commutative Moufang loop $Q$: 1) $Q$ satisfies the minimum condition for subloops; 2) if the loop $Q$ contains a centrally solvable subloop of class $s$, then it satisfies the minimum condition for centrally solvable subloops of class $s$; 3) if the loop $Q$ contains a centrally nilpotent subloop of class $n$, then it satisfies the minimum condition for centrally nilpotent subloops of class $n$; 4) $Q$ satisfies the minimum condition for noninvariant associative subloops. The structure of the commutative Moufang loops, whose infinite nonassociative subloops are normal is examined.