Abstract Algebra
Quiz
•
Mathematics
•
University
•
Practice Problem
•
Hard
Anthony Clark
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13 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Every group of prime order is abelian.
True
False
2.
MULTIPLE CHOICE QUESTION
1 min • 2 pts
Let a binary operation ‘*’ be defined on a set A. The operation will be commutative if ________
a*b=b*a
(b ο c)*a=(b*a) ο (c*a)
(a*b)*c=a*(b*c)
a*b=a
3.
MULTIPLE CHOICE QUESTION
1 min • 2 pts
What is an element of the group which can generate the rest of the elements of the group considering the properties that a group must satisfy?
Identitiy Element
Inverse Element
Group Generator
None of the Above
4.
MULTIPLE CHOICE QUESTION
1 min • 2 pts
Which is not a characteristic of a Klein-4 Group?
It is an Abelian Group.
The inverse of each element is itself.
It is a Cyclic Group.
The product of two elements is the other non-identity element.
5.
MULTIPLE CHOICE QUESTION
1 min • 2 pts
A homomorphism f: G→G’ is an isomorphism iff the kernel K is equal to _____.
{e}
G’
G
empty set
6.
MULTIPLE CHOICE QUESTION
1 min • 2 pts
Consider the binary operations on X, a*b = a+b+4, for a, b ∈ X. It satisfies the properties of _______.
NOT A GROUP
ABELIAN GROUP
GROUP
7.
MULTIPLE CHOICE QUESTION
1 min • 2 pts
In a group there must be only __________ identity element.
1
2
3
5
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