Permutations

**Juancd08** · October 16th 2008, 06:32 PM

In S_4, find a cyclic subgroup of order 4 and a non-cyclic one as well.

Let a and b belong to S_n. Prove that bab^-1 and a are both even or both odd.

**ThePerfectHacker** · October 16th 2008, 06:59 PM

Originally Posted by Juancd08

In S_4, find a cyclic subgroup of order 4 and a non-cyclic one as well.

$V = \{(1), (12)(34),(13)(24),(14)(23)\}$ .
And $\left< (1234) \right>$ are such examples.

Let a and b belong to S_n. Prove that bab^-1 and a are both even or both odd.

Hint: If $a=(a_1,...,a_k)$ then $bab^{-1} = (b(a_1),...,b(a_k))$ .

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