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Research articles

The commutative Moufang loops with minimum conditions for subloops II

N. I. Sandu

Tiraspol State University, Chişinău, Moldova

Abstract: 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.

Keywords and phrases: Commutative Moufang loops, minimum condition for nilpotent subloops, minimum condition for solvable subloops, minimum condition for noninvariant associative subloops.

MSC: 20N05

Received: 11.07.2004

Language: English

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