Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Algebra Class Equations, Sylow Theorems
Let p be a prime number. Let G be a group such that for each g ∈ G there exists an n ∈ ℕ such that gpn = 1. Which of the following statements is FALSE?
1
If |G| = p6, then G has a subgroup of index p2.
2
If |G| = p6, then G has at least five normal subgroups.
3
Center of G can be infinite.
4
There exists G with |G| = p6 such that G has exactly six normal subgroups.