It contains self explanatory questions and answers from the abstract algebra which covers a variety of topics of group theory. The format of the document is MCQs with answers. A student can easily understand the technique to answer such questions .
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
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller umershuaib. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $4.29. You're not tied to anything after your purchase.
