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Welcome to the Group Theory MCQs Page

Dive deep into the fascinating world of Group Theory with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Group Theory, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Group Theory, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Discrete Mathematics.

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Check out the MCQs below to embark on an enriching journey through Group Theory. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Group Theory. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Group Theory MCQs | Page 5 of 9

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Q41.
A trivial subgroup consists of ___________

a.

Identity element

b.

Coset

c.

Inverse element

d.

Ring

Discuss
Answer: (a).Identity element
Q42.
Minimum subgroup of a group is called _____________

a.

a commutative subgroup

b.

a lattice

c.

a trivial group

d.

a monoid

Discuss
Answer: (c).a trivial group
Q43.
Let K be a group with 8 elements. Let H be a subgroup of K and H<K. It is known that the size of H is at least 3. The size of H is __________

a.

8

b.

2

c.

3

d.

4

Discuss
Answer: (d).4
Q44.
__________ is not necessarily a property of a Group.

a.

Commutativity

b.

Existence of inverse for every element

c.

Existence of Identity

d.

Associativity

Discuss
Answer: (a).Commutativity
Q45.
A group of rational numbers is an example of __________

a.

a subgroup of a group of integers

b.

a subgroup of a group of real numbers

c.

a subgroup of a group of irrational numbers

d.

a subgroup of a group of complex numbers

Discuss
Answer: (b).a subgroup of a group of real numbers
Q46.
Intersection of subgroups is a ___________

a.

group

b.

subgroup

c.

semigroup

d.

cyclic group

Discuss
Answer: (b).subgroup
Q47.
The group of matrices with determinant _________ is a subgroup of the group of invertible matrices under multiplication.

a.

2

b.

3

c.

1

d.

4

Discuss
Answer: (c).1
Q48.
What is a circle group?

a.

a subgroup complex numbers having magnitude 1 of the group of nonzero complex elements

b.

a subgroup rational numbers having magnitude 2 of the group of real elements

c.

a subgroup irrational numbers having magnitude 2 of the group of nonzero complex elements

d.

a subgroup complex numbers having magnitude 1 of the group of whole numbers

Discuss
Answer: (a).a subgroup complex numbers having magnitude 1 of the group of nonzero complex elements
Q49.
A normal subgroup is ____________

a.

a subgroup under multiplication by the elements of the group

b.

an invariant under closure by the elements of that group

c.

a monoid with same number of elements of the original group

d.

an invariant equipped with conjugation by the elements of original group

Discuss
Answer: (d).an invariant equipped with conjugation by the elements of original group
Q50.
Two groups are isomorphic if and only if __________ is existed between them.

a.

homomorphism

b.

endomorphism

c.

isomorphism

d.

association

Discuss
Answer: (c).isomorphism
Page 5 of 9

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