True or false
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True or false
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.
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