Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!watmath!clyde!burl!ulysses!bellcore!decvax!ittatc!dcdwest!sdcsvax!ucbvax!nike!topaz!bentley!kwh
From: kwh@bentley.UUCP (KW Heuer)
Newsgroups: net.math
Subject: Re: not Groups
Message-ID: <641@bentley.UUCP>
Date: Sun, 16-Mar-86 15:19:57 EST
Article-I.D.: bentley.641
Posted: Sun Mar 16 15:19:57 1986
Date-Received: Wed, 19-Mar-86 00:48:23 EST
References: <886@ellie.UUCP>
Organization: AT&T Bell Laboratories, Liberty Corner
Lines: 14

In article <886@ellie.UUCP> ellie!colonel (Col. G. L. Sicherman) writes:
>The last book I read on Latin Squares called them "quasigroups" or
>something like that. "Loops" sounds much better--if they're indeed
>the same.

If I remember correctly, a loop is a quasigroup with an identity element.
The quasigroup axioms include cancellation (if xz=yz or zx=zy then x=y)
but not associativity; an associative quasigroup (or loop) is a group.
Another way to say this is that an object which is both a quasigroup and
a semigroup is a group.

What's the origin of the name "Loop"?  Is it a contraction of "Latin-
square group", or what?  (I see nothing that suggests roundness in either
loops or rings.)