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Soit n 2. (a) Demontrer que Sn est engendre par les transpositions (1 2), (1 3), . . . ,(1 n). (b) Demontrer que Sn
Soit n 2.
(a) Demontrer que Sn est engendre par les transpositions (1 2), (1 3), . . . ,(1 n).
(b) Demontrer que Sn est engendre par les transpositions (1 2), (2 3), . . . ,(n 1 n).
(c) On considere la transposition = (1 2) et le cycle c = (1 2 3 . . . n). Calculer ck tc-k .
(d) En deduire que Sn est engendre par et c.
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