Abstract Algebra: Permutation Groups Quiz

Sn contains a subgroup of order m, where 1 ≤ m ≤ n.

Sn contains a subgroup of order (n -1)!.

Sn is non-Abelian for all n ∈ N.

There exists a cycle of order m > 1, which belong to Z(Sn).

There exist three transpositions whose product is the identity e of the symmetric group Sn.

The order of the product of two transpositions is either 2 or 3.

If α and β are two disjoint permutations such that αβ = e, then α = β = e.

Every permutation in Sn can be expressed as a product of disjoint cycles.

(1 2)(1 3)(1 4)(2 5) is an even permutation.

An odd permutation is even.

(1 2 3 . . . n) is an odd permutation, if n is odd.

There exists a subgroup of Sn with index 2.

Option1

Option2

Option3

Option4

A subgroup H in S4, generated by (1 2 3) and (1 2) is of order 6.

The largest possible order of elements of the alternating group A5 is 10.

Each element in the alternating group A4 can be written as a product of 3-cycles,

There are exactly n!/2 odd permutations in Sn.