Question

Suppose Km={P∈Sm|, |P| is odd prime}. Determine the set for which m≥3 Km a subgroup of Sm.

(a) {3, 5, 7, 11, 13, …}

(b) {-14, -8, -3, 0, 3, 8, 14}

(c) {2, 4, 6, 8, 10, 12}

(d) {12, 25, 56, 78, 134,…}

I had been asked this question during an online interview.

This interesting question is from Permutation Groups topic in chapter Groups of Discrete Mathematics

Answer 1

Correct answer is (a) {3, 5, 7, 11, 13, …}

Easy explanation: Since Km is a subset of Sm, then the set will be {3, 5, 7, 11, 13, …}.