Groups Mock Tests

Let G be the group of all nonzero real numbers under multiplication. Which of the following is a normal subgroup of G?

The number of groups of order p² (where p is a prime) up to isomorphism is

Let G be the symmetric group S₄. The number of elements of order 2 in G is

The group Z₆ × Z₁₀ (direct product of cyclic groups) is isomorphic to

The number of elements in the symmetric group S₅ is

The order of the element 3 in the multiplicative group ℤ₇* is

Let G be the group of all permutations of a set with n elements, denoted Sₙ. For n ≥ 3, the center of Sₙ is