Group Theory

H and K are two subgroups of a group (G, .), then which of the following is a subgroup of G.

• H intersection K

• H union K

• Both 1 &2

In any group G, the number of identity elements is

• 2

• 1

• 0

Let H is a subgroup of G, then the identity of H is........

• Same as that of G.

• Not the identity in G

• Not in G

If H is a subgroup of a group G, then for any a, b in G, Ha=HB implies

• a=b

• ab`€H

• a'b€H

The number of generators of an infinite cyclic group is......

• 2

• 5

• Infinite

To define the quotient group G/N of a group G thenN must be ....

• Abelian Subgroup

• Subgroup

• Normal Subgroup

If p, q are any two elemts of a group G, then the equations px=q and yp=q have in G....

• No solution

• Unique solution

• Many solutions

The number of right cosets of any Subgroup of a finite group G is ..........the number of left cosets

• Greater than

• Equal to

• Less than