Purchase Solution

Description of Abelian group

Not what you're looking for?

Ask Custom Question

Modern Algebra
Group Theory (VII)

To prove that if G is an abelian group, then for all a,b belongs to G and all integers n, (a.b)^n=a^n.b^n.

The fully formatted problem is in the attached file.

Purchase this Solution

Solution Summary

This shows how to complete a proof regarding an Abelian group. The solution is detailed and well presented.

Solution Preview

The solution of the Posting is in the attached file.

Thanks for using BrainMass.com. Have a great day.
Prove that if is an abelian group, then for all and all integers , .

Proof:- Let be arbitrary.
By hypothesis, is an abelian group,

which imply that ---------------------------------(1)

which imply that

and
For

Suppose where is any integer, then

For

Hence by mathematical induction,

for all ...

Solution provided by:
Education
  • BSc, Manipur University
  • MSc, Kanpur University
Recent Feedback
  • "Thanks this really helped."
  • "Sorry for the delay, I was unable to be online during the holiday. The post is very helpful."
  • "Very nice thank you"
  • "Thank you a million!!! Would happen to understand any of the other tensor problems i have posted???"
  • "You are awesome. Thank you"
Purchase this Solution


Free BrainMass Quizzes
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

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.