Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Algebra Group & Subgroups
Consider a finite group G that is not simple and let |G| denote the order of group G. Which of the following is necessarily true?
1
If G is a non-abelian group and |G| is prime, then G contains nontrivial normal subgroups.
2
If G is abelian and |G| is prime, then G is only isomorphic to a group of rotations in 2D space.
3
If \(G= S_4\) then the sum of number of elements of order 2 and order 4 is 15.
4
If \(|G| = p^2\) (where p is a prime number), then G must be a simple group.