Basic of group theory

1. How many elements are there in the smallest non-trivial group?

• 1

• 2

• 3

• 4

If a group G has 6 elements, what is the order of the subgroup generated by an element of order 2?

• 1

• 2

• 3

• 6

For a group of order 10, what is the maximum possible order of a subgroup?

• 10

• 20

• 30

• 100

If a group G is cyclic of order 12, how many subgroups does G have?

• 1

• 5

• 7

• 3

The order of an element g in a group is 7. What is the order of the subgroup generated by g?

• 6

• 7

• 5

• 5

How many elements are there in the symmetric group S_3?

• 6

• 3

• Factorial 6

• Factorial 3

In the symmetric group S_4, how many 2-cycles (transpositions) are there?

What is the order of the element (1 2 3) in S_3?

How many distinct elements are in the alternating group A_4?

What is the order of the element (1 2 3) in S_3?