M. K. Kinyon and K. Kunen
The structure of extra loops

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.