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 7 of 9

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Q61.

Every cyclic group is a/an ______

infinite subgroup

abelian group

monoid

commutative semigroup

Discuss

Answer: (b).abelian group

Q62.

What is an irreducible module?

A cyclic module in a ring with any non-zero element as its generator

A cyclic module in a ring with any positive integer as its generator

An acyclic module in a ring with rational elements as its generator

A linearly independent module in a semigroup with a set of real numbers

Discuss

Answer: (a).A cyclic module in a ring with any non-zero element as its generator

Q63.

A finite group G of order 219 is __________

a semigroup

a subgroup

a commutative inverse

a cyclic group

Discuss

Answer: (d).a cyclic group

Q64.

The number of generators of cyclic group of order 219 is __________

144

124

218

Discuss

Answer: (a).144

Q65.

The order of a simple abelian group is __________

infinite

real number

finite

prime

Discuss

Answer: (a).infinite

Q66.

The Number of Elements Satisfying g7=e in a finite Group F is ______

even

not a number

odd

rational

Discuss

Answer: (c).odd

Q67.

All the rings of order p2 is ____________

associative

cyclic

inverse

commutative

Discuss

Answer: (d).commutative

Q68.

An element of a commutative ring R(1≠0) is nilpotent if __________

a+1=0

aⁿ = 0, for some positive integer n

aⁿ = 1, for some integer n

a² = 0

Discuss

Answer: (b).aⁿ = 0, for some positive integer n

Q69.

A group G of order 20 is __________

solvable

unsolvable

not determined

Discuss

Answer: (a).solvable

Q70.

Consider an integer 23 such that 23 >= 3p for a 2p-cycle in a permutation group, then p is ___________

odd prime

even prime

rational number

negative prime

Discuss

Answer: (a).odd prime

Page 7 of 9

Welcome to the Group Theory MCQs Page

Group Theory MCQs | Page 7 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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