1

Let $G=\{x,y│x^4=y^4=e,xyxy^{-1}=e\}$

1.Show that $|G|\leq 16$.

2.Suppose that $|G|=16$

a.Find $Z(G)$.

<p>b.Find a familiar group that is isomorphic to $G/〈y^2 〉$ and show that these are isomorphic.</p>

I am having trouble with part 2b. So far, I have Assume $|G|=16$ then $|G|/<y^2> = 8$ => $|G|/<y^2> = |D_4|$

I'm not sure which direction to head in after this. Any feedback is appreciated.

nonuser
  • 90,026
Kasha
  • 19
  • There only two nonabelian groups of order $8$: the dihedral group $D_8$ and the quaternion group $Q_8$. See https://groupprops.subwiki.org/wiki/Groups_of_order_8, which contains data that may help you differentiate between the two groups. – lhf Aug 25 '17 at 18:54

0 Answers0