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Articles

A new characterization of L2(p3)

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Pages 4000-4008 | Received 20 Aug 2021, Accepted 09 Mar 2022, Published online: 01 Apr 2022
 

Abstract

For a positive integer n and a prime p, let np denote the p-part of n. Let G be a group, cd(G) the set of all irreducible character degrees of G, ρ(G) the set of all prime divisors of integers in cd(G),V(G)={pep(G)pρ(G)}, where pep(G)=max{χ(1)pχIrr(G)}. The authors proved that GL2(p2) if and only if |G|=|L2(p2)| and V(G)=V(L2(p2)). In this paper, the authors continue this topic and prove that GL2(p3) if and only if |G|=|L2(p3)| and V(G)=V(L2(p3)).

2020 Mathematics Subject Classification:

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Grant Nos. 12071376, 11971391], Fundamental Research Funds for the Central Universities [No. XDJK2019B030].

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