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.

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 6 of 9

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Q51.

a * H is a set of _____ coset.

right

left

sub

semi

Discuss

Answer: (b).left

Q52.

a * H = H * a relation holds if __________

H is semigroup of an abelian group

H is monoid of a group

H is a cyclic group

H is subgroup of an abelian group

Discuss

Answer: (d).H is subgroup of an abelian group

Q53.

Lagrange’s theorem specifies __________

the order of semigroup is finite

the order of the subgroup divides the order of the finite group

the order of an abelian group is infinite

the order of the semigroup is added to the order of the group

Discuss

Answer: (b).the order of the subgroup divides the order of the finite group

Q54.

A function is defined by f(x)=2x and f(x + y) = f(x) + f(y) is called _____________

isomorphic

homomorphic

cyclic group

heteromorphic

Discuss

Answer: (a).isomorphic

Q55.

An isomorphism of a group onto itself is called ____________

homomorphism

heteromorphism

epimorphism

automorphism

Discuss

Answer: (d).automorphism

Q56.

The elements of a vector space form a/an ____________ under vector addition.

abelian group

commutative group

associative group

semigroup

Discuss

Answer: (a).abelian group

Q57.

A set of representatives of all the cosets is called _________

transitive

reversal

equivalent

transversal

Discuss

Answer: (d).transversal

Q58.

How many different non-isomorphic Abelian groups of order 8 are there?

Discuss

Answer: (c).2

Q59.

Consider the set B* of all strings over the alphabet set B = {0, 1} with the concatenation operator for strings ________

does not form a group

does not have the right identity element

forms a non-commutative group

forms a group if the empty string is removed from

Discuss

Answer: (a).does not form a group

Q60.

An infinite cyclic group does not have a ______ series.

Composite

Finite

Discuss

Answer: (c).Composite

Page 6 of 9

Welcome to the Group Theory MCQs Page

Group Theory MCQs | Page 6 of 9

Explore more Topics under Discrete Mathematics

Logics and Proofs

Sets and Functions

Sequences,Sums and Matrices

Algorithms

Number Theory and Cryptography

Induction and Recursion

Counting Theory

Discrete Probability

Relations

Graphs and Graphs Properties

Tree Properties

Boolean Algebra and Modeling Computations

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