Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Algebra Group & Subgroups
Which of the following is not true?
1
Let G is non-commutative group of order 2p, p is prime and there exists at least one element a of order p, then is normal in G.
2
Let G be a group in which (ab)3 = a3 b3 for all a, b ∈ G, then H = {x3 : x ∈ G} is normal subgroup of G
3
If H is normal subgroup of a finite group G, then [G:H] = 2.
4
Every commutative subgroup of a group is normal subgroup of the group