Purchase Solution

the definition of quaternion group

Not what you're looking for?

Ask Custom Question

(a) Show that the relations a^4 = 1, b^2 = a^2 and b^(-1)ab = a^(-1) define a group of order 8. (It is called the "quaternion group".)

(b) Show that this group is not isomporphic to Î"4 (also of order 8).

Please see the attachment for more precise text description.

Attachments
Purchase this Solution
Solution Summary

The definition of quaternion group is clearly reiterated.

Solution Preview

We have the definition of quaternion group as follows.

We also have anther non-abelian group with order 8. The group is called dehedral group defined as with the following ...

Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers

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

Graphs and Functions

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

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.

Solving quadratic inequalities

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

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

View More Free Quizzes
Related BrainMass Solutions

  • Generalized quaternion group

    isomorphic with either the dihedral group D_6 or the alternating group A_4 attached This provides proofs of several statements regarding a generalized quaternion group.

  • How do you show that G is not an abelian?

    Herstein This solution shows that the conclusion that the Quaternion group G is an abelian does not follow for the two consecutive integers with the relation (a.b)^i =a^i.b^i in an attached Word document.

  • Quaternion group presentation

    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 .

  • Semidirect product

    If sigma=(12) in S_n, n>=2, show that s_n is a semidirect product of A_n by Show that the dihedral group D_n= is a semidirect product of A= by B= Show that the quaternion group Q_2 cannot be expressed as

  • The quaternion group

    371292 The quaternion group Let G be a group generated by elements a and b such that |a| = 4, b^2 = a^2, and ba = a^3 b. Show that G is a group of order 8 and that G is isomorphic to the quaterunion group Q = {1, i, -1, -i, j, k, -j, -k }.

  • Problems in Group Theory and Quaternions

    of the quaternion is .

  • Ring of Integral Hamilton Quaternions and Isomorphisms

    Show that I(with multiplication) is isomorphic to the quaternion group of order 8 Please see the attached file for the complete solution. Thanks for using BrainMass. Ring of Integral Hamilton Quaternions and Isomorphisms are investigated.

  • Defining a group using axioms.

    28781 Definea Group using Axioms Define * on Z by a * b = max{a,b}. Is Z a group? No, Z is not a group under this definition. We can not find the identity of the group. If 0 is the identity, then (-1)*0=(-1).

  • Group

    339706 Group and self-identity What is a group, Explain the relationship between groups and a person's self-definition, a person's identity. Do groups help define who we are? A group consists of two or more people that come together for a purpose.

View More Related Solutions