The Structure of Extra Loops
نویسنده
چکیده
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.
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