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automorphisms of $u_{n}$ if $arphi_{d}(m)\in u$ for all $m\in u$. question: does the subgroups of order $p^{ }$ of $u_{n}$ are invariants under the diagonal automorphisms of $u_{n}$. abstract-algebra group-theory sylow-theory share | cite | improve this question asked hours ago nourr mga nourr mga bronze badges

for instance, take $$ h:=\left\{ egin{pmatrix} & a & & b\ & & & \ & & & a\ & & & \end{pmatrix} \mid a,b\in\mathbb{f}_p ight\}, $$ it is not conjugated to itself by $ ext{diag} ( , , )$. share | cite | improve this answer answered hours ago ancientmathematician ancientmathematician gold badge silver badges...

https://math.stackexchange.com/questions/3544882/on-subgroups-invariant-under-the-diagonal-automorphisms