Advanced Group Theory MCQs

Advanced Group Theory MCQs

University

20 Qs

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Advanced Group Theory MCQs

Advanced Group Theory MCQs

Assessment

Quiz

Mathematics

University

Practice Problem

Hard

Created by

Dr. Tiwari

Used 1+ times

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20 questions

Show all answers

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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