most recent 30 from http://mathoverflow.net 2013-05-23T07:07:29Z http://mathoverflow.net/feeds/question/100631 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/100631/small-problem-with-hamiltonian-groups Matt 2012-06-25T20:40:47Z 2012-06-25T20:40:47Z

<p>Alright, so I am studying Hamiltonian groups in the book "Theory of Groups" by Marshall Hall (specifically chapter 12, theorem 12.5.4). I have that $c = (a,b) = a^{-1}b^{-1}ab$ obeys that $(a^i,b) = c^i$. Now, I also have that every element is finite and, in paticular, that $a$ has order $N$ and $b$ has order $M$. The claim is that $a^p$, for $p$ a prime dividing $N$, commutes with $b$. I see no way how that should be the case and I would appriciate if someone could enlighten me.</p>