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Cayley tables and associativity

Published online by Cambridge University Press:  22 September 2016

R.P. Burn
R.P. Burn*
Affiliation:
Homerton College, Cambridge CB2 2PH
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Extract

Some of the group axioms are easy to check. The entries within the table are those outside, so the set is closed under the operation. The first row and column inside the table copy the row and column at the top and side, so 1 is a two-sided identity. A 1 appears in each row and each column of the table, and overall the 1 s appear symmetrically in the table, so each element has a two-sided inverse. The table is a latin square, so that, for given a and b, the equations ax = b and ya = b have unique solutions for x and y.

Type
Research Article
Information
The Mathematical Gazette , Volume 62 , Issue 422 , December 1978 , pp. 278 - 281
Copyright
Copyright © Mathematical Association 1978

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