BSc Practical Quiz

2.Let G denote the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication of G is a/an

• subgroup

• finite abelian group

• infinite, non-abelian group

• infinite abelian-group

1. 1. {1,i,-i,-1} is

• a semigroup

• not a group

• a non-abelian group

• a cyclic group

3. 3. Z is set of integers, forms a group if * is

• *(a, b)=a+b+2

• *(a, b )=2a+b

• *(a, b) = (a + b)/2

• *(a, b)=a^2 +b

4. 4. Let G be a group of order 6, and H be a subgroup of G such that 1 < |H| <6. Which one of the following options is correct?

• G is always cyclic, but H may not be cyclic

• G may not be cyclic, but H is always cyclic

• both G and H are always cyclic

• both G and H may not be cyclic

If (G,.) is a group such that (ab)^-1 =(a^-1)( b^-1), for all a, b belongs to G , then G is a/an

• Commutative semi-group

• abelian group

• non-abelian group

• none of these

6. 6. The number of generators of the cyclic group G of order 8 is

• 1

• 2

• 3

• 4