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Questions on group theory which concern finite groups.

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1 answer
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Finite $p$-groups of maximal class whose generators have order $p$

Let $G$ be a finite $p$-group of maximal nilpotency class that is not cyclic of order $p^2$. Then $G$ is $2$-generated, say $G=\langle a,b\rangle$. Is there a classification in the case when $a^p=b^p= …