HOMOMORPHISM OF GROUPS / COSETS / NORMAL SUBGROUPS – NAT – LEVEL – 2

If is a group homomorphism from to such that f(2) = 1/3, then the value of f(–8) is_____.

Let H be the set of all group homomorphism Then the order of H is _______.

Let G = D₄ (Dihedral group of order 8);   Then [D₄ : H] _____.

Let G = A₄. Let H = {(1), (12) (34)}. Then the index of H in G is ____.

Let    then   Hence n = ________.

The number of group homomorphism from the cyclic group   to the cyclic group is _____.

Let G = U(32), and H = {1, 31}. Then G/H is isomorphic to where n = _____.

Let G be a group,   be can element of order 24. How many left cosets in are there  _____.

The number of distinct normal subgroups of S₃ is ____.

For the divisors of |A₄|, there does not exist a subgroup of order ______ of A₄.