Groups

Which of the following is not necessarry for a set to be a group

• Associativity

• Closure

• Commutativity

• Existence of identity

Which of the following is NOT a group

• Set of all rationals with addittion

• Set of non zero reals with multiplication

• Set of all 2 x 3 matrices with matrix multiplication

• Set of all positive rational numbers with multiplication

• 3

• 4

• 6

• 10

• ba 

Identify the cyclic group

• center of G

• Trivial group

• Cyclic group

• Centraliser of g

• 3

• 4

• 5

• 6

Number of elements in alternating group of degree 6 is

• 1440

• 720

• 360

• 6