1261. The relation of conjugacy between elements of a group is :

A. Symmetric relation
B. Total order relation
C. Equivalence relation *
D. Lattice

1262. The relation of conjugacy between subgroups of a group is :

A. Symmetric relation
B. Equivalence relation *
C. Total order relation
D. Lattice

1263. Let H and K be two conjugate subgroups ofa group G . Then H and K are :

A. Finite
B. Isomorphic *
C. Infinite
D. Symmetric

1264. Let G be a group such that all of its subgroups are normal . then G can be :

A. Abelian Group
B. Hamiltonin Group
C. Identity Group
D. All of the above *

1265. A Subgroup of index 2 in a group is :

A. Normal *
B. Abelian
C. Symmetric
D. None

1266. Which of the following is a normal subgroup of Q of rational numbers w.r to additon :

A. Z *
B. N
C. W
D. R

1267. Let G be an abelian group. Then, at that point, which of the accompanying can be organization of G.

A. 5
B. 25
C. 49
D. All of the above *

1268. Let G be an abelian group. Then which of the accompanying can’t be organization of G:

A. 9
B. 16 *
C. 25
D. 121

1269. Let G be a group. The set of all automorphism A(G) is a :

A. Semi Group
B. Group *
C. Normal Subgroup
D. None

1270. Which of the following group has all of its automorphism are inner automorphism :

A. S3 *
B. Z
C. Q
D. R