Discussion:
Name of an operator-set combination
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Diamond, Mark
2006-11-24 02:56:33 UTC
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Could someone please tell me if the operator-set combination, where the
operator is commutative but NOT associative, has any special name. For
example, (fixed font makes this look correct) ...

. | 0 | 1 | 2 | 3 |
-------------------
0 | 0 3 2 1
1 | 3 1 0 2
2 | 2 0 1 3
3 | 1 2 3 0

If it does, I'd very much like to know what it is.

Cheers,

Mark Diamond
Ken Pledger
2006-12-12 21:10:46 UTC
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Post by Diamond, Mark
Could someone please tell me if the operator-set combination, where the
operator is commutative but NOT associative, has any special name. For
example, (fixed font makes this look correct) ...
. | 0 | 1 | 2 | 3 |
-------------------
0 | 0 3 2 1
1 | 3 1 0 2
2 | 2 0 1 3
3 | 1 2 3 0
If it does, I'd very much like to know what it is.
Cheers,
Mark Diamond
It's just a commutative groupoid, although your particular example
happens to be a commutative quasigroup. (In a quasigroup the equation
xy = z determines each of x, y, z uniquely from the other two.)

I'm sorry this reply is so late. If you'd like to post to news
groups carrying more traffic than <aus.mathematics>, you might like to
try <sci.math> or <alt.math.undergrad>.

Ken Pledger.

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