ALGEBRA-1

Which one of the following is not a group?

• The set of natural numbers with usual addition as binary operation.

•   The set of complex numbers whose modulus is 1 with respect to multiplication of complex numbers.

• The set  with respect to addition modulo .

• The power set of non-empty set X with symmetric difference of sets as binary operation.

• 2

• 4

• 6

• 8

Let H and K be two subgroups of a group G such that H has 7 elements and K has 13 elements. Then the number of elements of HK is

• 6

• 20

• 91

• 1

• 5

• -5

• -6

• -7

• b

• 90

• 225

• 120

• 160

• 2

• 5

• 6

• Infinite

• a

• ab

• b

If every element of a group G be its own inverse, then the group G is

• of infinite order

• non-commutative

•   commutative

• none of these.

• 3

• 6

• 8

• 5