The commutative Moufang loops with minimum conditions for subloops I

N. I. Sandu

The commutative Moufang loops with minimum conditions for subloops I

Rings and Algebras 2008-04-25 v1

Authors: N. I. Sandu

Abstract

The structure of the commutative Moufang loops (CML) with minimum condition for subloops is examined. In particular it is proved that such a CML $Q$ is a finite extension of a direct product of a finite number of the quasicyclic groups, lying in the centre of the CML $Q$ . It is shown that the minimum conditions for subloops and for normal subloops are equivalent in a CML. Moreover, such CML also characterized by different conditions of finiteness of its multiplication groups.

Cite

@article{arxiv.0804.3956,
  title  = {The commutative Moufang loops with minimum conditions for subloops I},
  author = {N. I. Sandu},
  journal= {arXiv preprint arXiv:0804.3956},
  year   = {2008}
}