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In this paper we give two new characterizations for the sporadic
simple groups, based on the orders of the normalizers of the Sylow
subgroups. Let $\textit{S}$ be a sporadic simple group and
$\textit{p}$ be the greatest prime divisor of $|\textit{S}|$. In
this paper we prove that ${S}$ is uniquely determined among finite
groups by $|S|$ and $|N_{S}(\textit{P})|$, where $\textit{P}\in$
Syl$ _{p}(S)$. Also we prove that if $\textit{G}$ is a finite
group. then $\textit{G}\cong{S}$ if and only of for every prime
$q,|N_{S}(Q)|=|N_{G}(\textit{Q}')|$, where $\textit{Q}\in$
Syl$_{q}(S)$ and $\textit{Q}'\in$ Syl$_{q}(G)$.
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