Golden Questions of Group Theory

Choose the appropriate choice in each of the following case.
Sr. Course Code Questions Text Score
1 Every group of order pq ( p<q) is ________
Abelian 0
Simple 0
Nilpotent 0
Solvable 1
2 A group G is said to be nilpotent if G has a _________
Central series 1
Composition Series 0
Chief series 0
Normal series 0
3 𝐷𝑛 is nilpotent if and only if ______
n  2i , i  0 1
n  5i , i  0 0
n  2i , i  0 0
n  3i , i  0 0
22 The group Zn is_____
Non-Abelian 0
Simple 0
Non-Cyclic 0
Solvable 1
4 Which of the following is not an order of a non abelian group
6 0
9 1
12 0
14 0
7 The special linear group is ________
SL( n, R )  { A  GL( n, R ) : det( A)  1} 1
SL ( n, R )  { A  GL( n, R ) : det( A)  1} 0
SL(n, R)  { A  GL(n, R) : det( A)  1} 0
SL(n, R)  { A  GL(n, R) : det( A)  1} 0
5 A nilpotent group is a group that has _____ which terminates with G.

, Upper central series 1
Lower central series 0
Composition series 0
Central series 0
6 The commutator subgroup of 𝑄is8_______
<i> 0
{1} 0
𝑄8 0
{1,-1} 1
10 Z [ SL(n, R)]  ________
{ I n } 0
{ I n } 0
{ I n } 1
SL(n,R) 0
9 Which of the following group is solvable but not nilpotent?
𝑆3 1
𝐴3 0
𝑉4 0
U(8) 0
10 | SL(2,3) | ?
6 0
12 0
24 1
30 0
11 The smallest non abelian group has order _____
5 0
6 1
7 0
9 0
12 Every group of order _____ is abelian
𝑝2 1
𝑝3 0
2p 0