Let $G$ be a group of order $9$ generated by two elements $a$ and $b$ such that $a^3 = b^3 =e$.
How to determine all possible automorphisms of $G$?
2026-03-26 13:02:22.1774530142
What are all the automorphisms of a group of order $9$ generated by two elements?
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Show $G \cong \mathbb{Z}/3\mathbb{Z} \times \mathbb{Z}/3\mathbb{Z}$.
Regard this as a $2$-dimensional vector space over $\mathbb{F}_3$.
Apply what you know from linear algebra.