True or false
Posted: Sat Feb 04, 2017 5:46 pm
Examine if the following is true.
If \(\displaystyle{p}\) is a prime number and\(\displaystyle{\left(G,\cdot\right)}\) is a group
such that \(\displaystyle{o(G)=p^3}\) and \(\displaystyle{x^p=1\,,\forall\,x\in G}\) then
\(\displaystyle{\left(G,\cdot\right)}\) is abelian.
If \(\displaystyle{p}\) is a prime number and\(\displaystyle{\left(G,\cdot\right)}\) is a group
such that \(\displaystyle{o(G)=p^3}\) and \(\displaystyle{x^p=1\,,\forall\,x\in G}\) then
\(\displaystyle{\left(G,\cdot\right)}\) is abelian.