RO  EN
IMCS/Publications/QRS/Issues/QRS v.12, n.1 (12), 2004/

The structure of extra loops

Authors: M. K. Kinyon, K. Kunen

Abstract

The Sylow theorems hold for finite extra loops, as does P. Hall's theorem for finite solvable extra loops. Every finite nonassociative extra loop Q has a nontrivial center, Z(Q). Furthermore, Q/Z(Q) is a group whenever |Q|512. Loop extensions are used to construct an infinite nonassociative extra loop with a trivial center and a nonassociative extra loop Q of order 512 such that Q/Z(Q) is nonassociative. There are exactly 16 nonassociative extra loops of order 16p for each odd prime p.

Michael K. Kinyon
Department of Mathematical Sciences,
Indiana University South Bend,
South Bend, IN 46634 USA.
E-mail:
http://mypage.iusb.edu/~mkinyon
___________________________
Kenneth Kunen
Department of Mathematics,
University of Wisconsin,
Madison, WI 57306 USA.
E-mail:
http://www.math.wisc.edu/~kunen



Fulltext

Adobe PDF document0.33 Mb