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IMI/Publicaţii/BASM/Ediţii/BASM n.2 (45), 2004/

The commutative Moufang loops with minimum conditions for subloops II.

Authors: N.I. Sandu

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. f 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;


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