What's the meaning of the adjective 'alternating' in the name of the 'alternating group' ? 



Meaning of 'alternating' group ? 
Evidence for Brendan McKay's suggestion that it comes from the older concept of an [alternating polynomial](http://en.wikipedia.org/wiki/Alternating_polynomial) may be found in Burnside's classic book, *Theory of Groups of Finite Order*. When defining the symmetric and alternating groups, he puts an asterisk next to the word "alternating" and adds the following footnote:



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> The symmetric group has been so called because the only functions of the $n$ symbols which are unaltered by all the substitutions of the group are the symmetric functions. All the substitutions of the alternating group leave the square root of the discriminant unaltered.
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By "the square root of the discriminant," Burnside means the polynomial
$$\prod\_{r=1}^{n-1}\prod\_{s=r+1}^n (a\_r-a\_s),$$
which of course is an alternating polynomial.


