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We know all 2-transitive simple groups by Dixon's book (Permutation groups). Now let $G$ be finite simple group $2$-transitive and $p(p^{2}-1)/2$ divides order $G$ and also $\pi (p(p^{2}-1))\subseteq \pi (L_{2}(p))$$\pi (G)\subseteq \pi (p(p^{2}-1))$. Is it true $G$ isomorphic to $L_{2}(p)$?

We know all 2-transitive simple groups by Dixon's book (Permutation groups). Now let $G$ be finite simple group $2$-transitive and $p(p^{2}-1)/2$ divides order $G$ and also $\pi (p(p^{2}-1))\subseteq \pi (L_{2}(p))$. Is it true $G$ isomorphic to $L_{2}(p)$?

We know all 2-transitive simple groups by Dixon's book (Permutation groups). Now let $G$ be finite simple group $2$-transitive and $p(p^{2}-1)/2$ divides order $G$ and also $\pi (G)\subseteq \pi (p(p^{2}-1))$. Is it true $G$ isomorphic to $L_{2}(p)$?

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R K
R K
  • 224
  • 2
  • 5

A group 2-transitive

We know all 2-transitive simple groups by Dixon's book (Permutation groups). Now let $G$ be finite simple group $2$-transitive and $p(p^{2}-1)/2$ divides order $G$ and also $\pi (p(p^{2}-1))\subseteq \pi (L_{2}(p))$. Is it true $G$ isomorphic to $L_{2}(p)$?