Recent content by NeoAkaTheOne

You're correct. Small oversight, but I think I meant ##Q\times \mathbb{Z}/2\mathbb{Z}## with ##Q## being the quaternion group. Surely that doesn't have an element of order ##8##?

Ah, the question was not very eloquently phrased. To answer the question, mircomass is correct in saying that the smallest example comes with order ##16##. Consider ##\mathbb{Z}/8\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}\not\simeq\mathbb{Z}/4\mathbb{Z}\times\mathbb{Z}/4\mathbb{Z}\not\simeq H##...

##\mathbb{Z}_p## (also denoted as the quotient group ##\mathbb{Z}/p\mathbb{Z})## is the set of residue classes modulo ##p##. So for example, ##\mathbb{Z}_5=\{0,1,2,3,4\}##. In the above example, ##\rtimes## denotes the semi direct product, as opposed to ##\times## which is the direct product...