Given a cycle $c in S_n $ with $ ord(c) = s $ and $ s = kt $, prove that $c^k$ is a product of $k$ cycles of...
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I came across this question in a recent exam. Given that $ ord(c) = s $ , we assume that $c^s = c^{kt} = (id) implies (c^{k})^t = (id)$ . That means that $c^k$ is a cycle of order $t$ . Can you please help me on the next step?
abstract-algebra group-theory permutations permutation-cycles
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edited Jan 16 at 16:17
ntua_math
asked Jan 16 at 15:17
ntua_math ntua_math
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