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Generalized quaternion group

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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 isomorphic with either the dihedral group D_6 or the alternating group A_4

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Solution Summary

This provides proofs of several statements regarding a generalized quaternion group.

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