
Advanced Group Theory MCQs
Quiz
•
Mathematics
•
University
•
Practice Problem
•
Hard
Dr. Tiwari
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20 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Let G be a finite group and p be a prime dividing |G|. Then which of the following statements is always true?
G has a unique subgroup of order p
G has a subgroup of order p
G is cyclic
Every subgroup of order p is normal
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If G is a finite group and H is a subgroup of G with index 2, then:
H is cyclic
H is trivial
H is normal in G
H is the center of G
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Let G be a finite group such that G/Z(G) is cyclic. Then G is:
Simple
Cyclic
Abelian
Nilpotent
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In a finite group, the number of elements conjugate to an element g is equal to:
Order of g
Index of the centralizer C_G(g)
Order of C_G(g)
Order of Z(G)
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Let G be a group of order 231. The number of Sylow 11-subgroups in G is:
1
3
7
21
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The number of elements of order 5 in S5 is:
12
24
0
20
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Let G be a group of order 56. The number of Sylow 7-subgroups in G can be:
1 or 8
2 or 4
1, 2, 4 or 8
Only 1
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