I have a cyclic permutation group G=<(123456)> what is normalizer of this group?
the normalizer a subset A of a group G such that:
$$N_{G}(A)= (g \in G s.t \;\;\; gag^{-1} \in A , \;\; \forall a \in A)$$
2026-03-29 04:48:20.1774759700
normalizer of a cyclic group
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Hint: For any $\sigma\in S_6$, we have $$\sigma(123456)\sigma^{-1}=(\sigma(1)\sigma(2)\sigma(3)\sigma(4)\sigma(5)\sigma(6)),$$ where $\sigma(i)$ is $\sigma$ applied to $i$.