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Let q$q$ be odd, G=PSU_n(q) $G=PSU_n(q)$ (Projective Special Unitary group) and H=PSU_{n-1}(q)$H=PSU_{n-1}(q)$. Is it always true that H$H$ is a subgroup of G?$G\ ?$

Let q be odd, G=PSU_n(q) (Projective Special Unitary group) and H=PSU_{n-1}(q). Is it always true that H is a subgroup of G?

Let $q$ be odd, $G=PSU_n(q)$ (Projective Special Unitary group) and $H=PSU_{n-1}(q)$. Is it always true that $H$ is a subgroup of $G\ ?$

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darya
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question about projective special unitary group

Let q be odd, G=PSU_n(q) (Projective Special Unitary group) and H=PSU_{n-1}(q). Is it always true that H is a subgroup of G?