Homomorphisms and Mapping Prime Elements
Not what you're looking for?
Let G and H be two finite cyclic groups of relatively prime orders. Determine the number of homomorphisms from G to H.
Purchase this Solution
Solution Summary
Homomorphisms and Mapping Prime Elements are investigated.
Solution Preview
The number of such homomorphisms is zero (0).
----------
Why?
Reason by intuition: You should smell something wrong or at least
your antennas should vibrate whenever there are two cyclic groups
of unrelated orders. How to confirm your instincts?
Proof by contradiction:-
Suppose G has m elements and identity element e.
Suppose H has n elements and identity element 1.
Suppose there were such a thing as a homomorphism
f : G ----> H
Let g be a generator for G and h be the image of g under
this purported homomorphism.
f : e |---> 1
f : g ...
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Probability Quiz
Some questions on probability
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts