Definition of a group.

Exploring Group Theory Concepts

Quiz
•
Mathematics
•
University
•
Easy
Dr. Tiwari
Used 2+ times
FREE Resource
20 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A group is a collection of numbers only.
A group must have at least three elements.
A group is a set with a binary operation satisfying closure, associativity, identity, and invertibility.
A group is defined by its geometric properties.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the criteria for a subset to be a subgroup?
A subset must contain at least two elements to be a subgroup.
A subset is a subgroup if it is closed under the group operation only.
A subset H is a subgroup if it contains the identity, is closed under the group operation, and is closed under inverses.
A subset is a subgroup if it is non-empty and contains all group elements.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The concept of a group homomorphism.
A group homomorphism is a type of group that contains subgroups.
A group homomorphism is a function between two groups that preserves the group operation.
A group homomorphism is a mapping that only applies to finite groups.
A group homomorphism is a function that changes the group operation completely.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you solve the equation x * a = b in a group?
x = b * a^(-1)
x = b + a
x = b / a
x = a * b
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a group action and how is it defined?
A group action is a type of mathematical operation on numbers.
A group action is a visual representation of group elements.
A group action is a method of combining two groups into one.
A group action is a function from a group G and a set X to X, denoted as G × X → X, satisfying specific properties.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Classify the group Z_6 and describe its structure.
Z_6 is a cyclic group of order 6.
Z_6 is a finite abelian group of order 4.
Z_6 has an order of 12.
Z_6 is a non-cyclic group of order 6.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the identity element in a group?
The identity element is the element that can only be combined with itself.
The identity element in a group is the element that leaves other elements unchanged when combined.
The identity element is the largest element in the group.
The identity element is the element that always changes other elements.
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