Assignment:
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.
Provide complete and step by step solution for the question and show calculations and use formulas.