This article is cited in 5 papers

Commutative Moufang Loops with Finite Conjugacy Classes of Subloops

N. I. Sandu

State Agricultural University of Moldova

Abstract: It is proved that the following conditions are equivalent for an arbitrary commutative Moufang loop $Q$:

• 1) the loop $Q$ is finite over the center;
• 2) every subloop of $Q$ defines a finite conjugacy class of subloops;
• 3) every associative subloop of $Q$ defines a finite conjugacy class of subloops;
• 4) every infinite associative subloop of $Q$ defines a finite conjugacy class of subloops.

UDC: 519.48

Received: 07.12.1999

DOI: 10.4213/mzm186

 English version: Mathematical Notes, 2003, 73:2, 249–258

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