Abstract algebra mid(2)

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

• H intersection K

• H union K

• Both 1 and 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......

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

• 2

• 5

• Infinite

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

• Abelian Subgroup

• Subgroup

• Normal Subgroup

If p,q are any two elements 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

If a is a generator of a cyclic group G, then........is also a generator of G

• a square

• a inverse

• a cube

If a finite group of order n contains an element of order n, then the group must be ....

• Abelian

• Normal Subgroup

• Cyclic