I know that $a$ and $b$ are generators of a group $G$ and $a^{3^3}=b^9=1$.
- Are these informations sufficient to affirm that the group is a $3$-group?
- Adding the relation $b^{-1}ab=a^4$, can we state that it is a $3$-group?
I know that $a$ and $b$ are generators of a group $G$ and $a^{3^3}=b^9=1$.