The quaternion group

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• Generalized quaternion group

  238577 Generalized quaternion group Define the generalized quaternion group by the presentation Q_n = < a,b|a^2n=1, b^2=a^n, ab=ba^-1 > for n >=1 Show that |Q_n|=4n Show that Q_1 is cyclic and Q_2 is the quaternion group Show that Q_3 is not

• the definition of quaternion group

  399372 the definition of quaternion group (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".)

• 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

  238575 Quaternion group presentation Show that the quaternion group Q_2 = {+1, -1, +i, -i, +j, -j, +k, -k} has presentation I need a rigorous proof with explanations so that I can study and understand please.

• 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

• 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.

• group communication

  What aspects of group communication will you keep in mind and what steps will you take to interact effectively in the group? 2) The company you are working in has assigned you the task of leading a group. Your group has to solve a problem.

• Definitions and Examples : Groups, Abelian Groups and Non-Abelian Groups

  simplest non-Abelian group is the dihedral group D3, which is of group order six.