Purchase Solution

Quaternion group presentation

Not what you're looking for?

Ask Custom Question

Show that the quaternion group Q_2 = {+1, -1, +i, -i, +j, -j, +k, -k} has presentation <a,b|a^4 =1, a^2 = b^2, ab = ba^3>

I need a rigorous proof with explanations so that I can study and understand please. I have an exam on Thursday.

Purchase this Solution

Solution Summary

This solution is comprised of a detailed explanation to show that the quaternion group Q_2 = {+1, -1, +i, -i, +j, -j, +k, -k} has presentation <a,b|a^4 =1, a^2 = b^2, ab = ba^3>.

Solution Preview

Recall the following useful result:

Let X be a set and Y a set of reduced words on X and let G = <X | Y>.

If H is any group with H = <X>, and H satisfies all the relations (in Y), then ...

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.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

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

Probability Quiz

Some questions on probability

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.