A new characterization of L2(p2)
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})) .
1989 ◽
Vol 41
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pp. 68-82
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2005 ◽
Vol 284
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pp. 326-332
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2015 ◽
Vol 45
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pp. 1645-1658
2019 ◽
Vol 46
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pp. 1073-1081
2019 ◽
Vol 19
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pp. 2050036
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1987 ◽
Vol 24
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pp. 838-851
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