CSIR NET Maths previous year question papers

Single choice · Groups

1. A

   If |G| $= p^{6}$, then G has a subgroup of index $p^{2}$.

2. B

   If |G| $= p^{6}$, then G has at least five normal subgroups.

3. C

   Center of G can be infinite.

4. D

   There exists G with |G| $= p^{6}$ such that G has exactly six normal subgroups.

Single choice · Groups

1. A

   G is a union of proper subgroups.

2. B

   G is a union of proper subgroups if |G| has at least two distinct prime divisors.

3. C

   If G is abelian, then G is a union of proper subgroups.

4. D

   G is a union of proper subgroups if and only if G is not cyclic.