Test: Group Theory - 8 - Mathematics MCQ

If A, B, and C are invertible matrices, the expression (AB^-1)^-1(CA^-1)^-1C² evaluates to 

Let G be the group of all symmetries of the square. Then, the number of conjugate classes in G is

S₅ be the permutation group on 5 symbols. Then, number of elements in S₅, s.t. a⁵ = a² are

 I f given permutation are A =  then find BA.

The number of elements of order 5 in a non-abelian group of order 10 is

Let G be group of order 1225, then G is

If a cyclic group has only 3 subgroups {e}, a subgroup of order 7 and the group itself. Then, the order of group is

The number of abelian groups of order 20 upto isomorphism is

If G is a group of even order, then it has element of order two

For any integer n > 2 how many elements in U(rt) that satisfy x²= 1

The set of four rotations of a square of its plane about a normal passing through the centre of the plane form a

The number of conjugate classes of a non-abelian group of order 125 are

 A finitely generated subgroup G of additive group Q of rational numbers satisfies the condition

The number of element of order 11 in a group of order 33 are

The number of element of order 2 in a cyclic group of even order is

 The number of homomorphism from Z₁₂ to Z₃₀ are