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A new characterization for the simple group ${\rm PSL}(2,p^2)$ by order and some character degrees
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 271-280
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Let $G$ be a finite group and $p$ a prime number. We prove that if $G$ is a finite group of order $|{\rm PSL}(2,p^2)|$ such that $G$ has an irreducible character of degree $p^2$ and we know that $G$ has no irreducible character $\theta $ such that $2p\mid \theta (1)$, then $G$ is isomorphic to ${\rm PSL}(2,p^2)$. As a consequence of our result we prove that ${\rm PSL}(2,p^2)$ is uniquely determined by the structure of its complex group algebra.
Let $G$ be a finite group and $p$ a prime number. We prove that if $G$ is a finite group of order $|{\rm PSL}(2,p^2)|$ such that $G$ has an irreducible character of degree $p^2$ and we know that $G$ has no irreducible character $\theta $ such that $2p\mid \theta (1)$, then $G$ is isomorphic to ${\rm PSL}(2,p^2)$. As a consequence of our result we prove that ${\rm PSL}(2,p^2)$ is uniquely determined by the structure of its complex group algebra.
DOI : 10.1007/s10587-015-0173-6
Classification : 20C15, 20C33, 20D05, 20D06, 20D60
Keywords: character degree; order; projective special linear group 
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     title = {A new characterization for the simple group ${\rm PSL}(2,p^2)$ by order and some character degrees},
     journal = {Czechoslovak Mathematical Journal},
     pages = {271--280},
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Khosravi, Behrooz; Khosravi, Behnam; Khosravi, Bahman; Momen, Zahra. A new characterization for the simple group ${\rm PSL}(2,p^2)$ by order and some character degrees. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 271-280. doi: 10.1007/s10587-015-0173-6

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