Abstract
For a positive integer n and a prime p, let
{n}_{p}
denote the p-part of n. Let G be a group,
\text{cd}(G)
the set of all irreducible character degrees of
G
,
\rho (G)
the set of all prime divisors of integers in
\text{cd}(G)
,
V(G)=\left\{{p}^{{e}_{p}(G)}|p\in \rho (G)\right\}
, where
{p}^{{e}_{p}(G)}=\hspace{.25em}\max \hspace{.25em}\{\chi {(1)}_{p}|\chi \in \text{Irr}(G)\}.
In this article, it is proved that
G\cong {L}_{2}({p}^{2})
if and only if
|G|=|{L}_{2}({p}^{2})|
and
V(G)=V({L}_{2}({p}^{2}))
.
On the maximal length of two sequences of consecutive integers with the same prime divisors