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ICMC 2018/19 Round 2, Problem 2

Source: Imperial College Mathematics Competition 2018/19 - Round 2

August 7, 2020
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Problem Statement

In the symmetric group Sn (n≥3)S_n\ (n \geq 3), let Ga,bG_{a,b} be the subgroup generated by the 2-cycle (a b)(a\ b) and the n-cycle (1 2 ⋯ n)(1\ 2\ \cdots\ n). Find the index ∣Sn:Ga,b∣\left|S_n : G_{a,b}\right|.
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