abstract algebra iii

abstract algebra iii

University

6 Qs

quiz-placeholder

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abstract algebra iii

abstract algebra iii

Assessment

Quiz

Mathematics

University

Hard

Created by

MANJULA D

FREE Resource

6 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

Remembering: What is the second part of Sylow's Theorem?
There exists a Sylow p-subgroup for every prime number p
Every Sylow p-subgroup is normal
The number of Sylow p-subgroups is congruent to 1 mod p
The number of Sylow p-subgroups divides the order of the group

2.

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Understanding: What does it mean for a Sylow p-subgroup to be normal in a group?
The Sylow p-subgroup is the only subgroup of its order
The Sylow p-subgroup is unique and has p elements
Every element of the group normalizes the Sylow p-subgroup
The Sylow p-subgroup is the unique subgroup of its order and has p elements

3.

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Applying: If a group has 90 elements and is known to have a Sylow 3-subgroup, what can be said about the number of elements in the Sylow 3-subgroup?
It has 3 elements
It has 9 elements
It has 27 elements
It has 81 elements

4.

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Analyzing: How does the second part of Sylow's theorem help to classify groups?
By determining if a group is abelian
By determining the number of normal subgroups in a group
By determining the number of Sylow p-subgroups in a group
By determining the order of a group

5.

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Evaluating: Can the second part of Sylow's theorem be used to determine if a group is simple?
No, the second part of Sylow's theorem does not address simplicity
Yes, if there is only one normal Sylow p-subgroup for every prime number p
No, the second part of Sylow's theorem only deals with the normality of Sylow p-subgroups
Yes, if the number of normal Sylow p-subgroups is equal to the order of the group

6.

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Creating: Can the second part of Sylow's theorem be used to determine if a group is abelian?
No, the second part of Sylow's theorem only deals with the normality of Sylow p-subgroups
Yes, if every Sylow p-subgroup is normal
No, the second part of Sylow's theorem does not address the abelian property
Yes, if there is only one normal Sylow p-subgroup for every prime number p