Talk:Zolotarev's lemma
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An example which isn't an example[edit]
The article currently says
This interpretation of the Legendre symbol as the sign of a permutation can be extended to the Jacobi symbol ... where a and n are relatively prime odd integers with n > 0: ... For example, multiplication by 2 on Z/21Z has cycle decomposition ... and the Jacobi symbol (2|21) is −1.
Since 2 is not an odd integer, this isn't an example of the extension which it says it's an example of. In fact, it seems to be an example of a still stronger generalisation. What's the correct statement of the extension? 95.17.84.95 (talk) 13:16, 8 December 2015 (UTC)
Another proof[edit]
To me it's unclear from where the author infers the assertion "But W is even, ..." in the last line of the proof. — MFH:Talk 20:49, 18 November 2020 (UTC)
Two answers[edit]
The remark on the incorrect example is correct. The proper statement requires only n to be odd.
W is even because it acts the same on each of the two rows in the matrix. 131.155.95.134 (talk) 08:19, 2 September 2021 (UTC)