Cauchy Number of Permutation (REA Practice Test 3, #62)

Forum for the GRE subject test in mathematics.
Ellen
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Joined: Sat Aug 10, 2013 3:56 pm

Cauchy Number of Permutation (REA Practice Test 3, #62)

Postby Ellen » Mon Sep 16, 2013 1:40 pm

Can anyone tell me the purpose and/or derivation of the "Cauchy number" of a permutation of a symmetric group, REA GRE Practice Test 3, Prob. #62? Cauchy made a lot of numbers.... (Overacheiver. 8)) The only one I can find anywhere is in physics, although obviously I'm sure this one is closely related to his theorem about orders of groups.

(Paraphrased) "If Sn is split into n disjoint subgroups of orders a1, a2...an, the Cauchy number is Sum[i=1 to n] {ai-1}.

This is all the explanation given. The computation is easy, but I don't understand why I'm doing it. It's not describing the number of generators according to the permutation, is it?

Thanks!



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