English

On the commutative center of Moufang loops

Group Theory 2021-04-20 v1

Abstract

We construct two infinite series of Moufang loops of exponent 33 whose commutative center (i.e. the set of elements that commute with all elements of the loop) is not a normal subloop. In particular, we obtain examples of such loops of orders 383^8 and 3113^{11} one of which can be defined as the Moufang triplication of the free Burnside group B(3,3)B(3,3).

Keywords

Cite

@article{arxiv.1711.07001,
  title  = {On the commutative center of Moufang loops},
  author = {Alexander N. Grishkov and Andrei V. Zavarnitsine},
  journal= {arXiv preprint arXiv:1711.07001},
  year   = {2021}
}