Výsledky vyhledávání - "20C15, 20D05"

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A characterization of some finite simple groups by their character codegrees

Autor: Tong-Viet, Hung P.

For a finite group $G$ and an irreducible complex character $\chi$ of $G$, the codegree of $\chi$ is defined by $\textrm{cod}(\chi)=|G:\textrm{ker}(\chi)|/\chi(1)$, where $\textrm{ker}(\chi)$ is the kernel of $\chi$. In this paper, we show that if $H

Externí odkaz: http://arxiv.org/abs/2406.17794

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p-Regular conjugacy classes and p-rational irreducible characters

Autor: Hung, Nguyen Ngoc, Maroti, Attila

Let $G$ be a finite group of order divisible by a prime $p$. The number of $p$-regular and $p'$-regular conjugacy classes of $G$ is at least $2\sqrt{p-1}$. Also, the number of $p$-rational and $p'$-rational irreducible characters of $G$ is at least $

Externí odkaz: http://arxiv.org/abs/2004.05194

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Finite groups with an automorphism inverting, squaring or cubing a non-negligible fraction of elements

Autor: Bors, Alexander

There are various results in the literature which are part of the general philosophy that a finite group for which a certain parameter (for example, the number of conjugacy classes or the maximum number of elements inverted, squared or cubed by a sin

Externí odkaz: http://arxiv.org/abs/1601.04311

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On groups with the same character degrees as almost simple groups with socle the Mathieu groups

Autor: Alavi, Seyed Hassan, Daneshkhah, Ashraf, Jafari, Ali

Let $G$ be a finite group and $cd(G)$ denote the set of complex irreducible character degrees of $G$. In this paper, we prove that if $G$ is a finite group and $H$ is an almost simple group whose socle is Mathieu group such that $cd(G) =cd(H)$, then

Externí odkaz: http://arxiv.org/abs/1511.04129

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Huppert's Conjecture for Alternating groups

Autor: Bessenrodt, Christine, Tong-Viet, Hung P., Zhang, Jiping

We prove that the alternating groups of degree at least $5$ are uniquely determined up to an abelian direct factor by the degrees of their irreducible complex representations. This confirms Huppert's Conjecture for alternating groups.
Comment: 2

Externí odkaz: http://arxiv.org/abs/1502.03425

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Nilpotent and Abelian Hall Subgroups in Finite Groups

Autor: Beltrán, Antonio, Felipe, María José, Malle, Gunter, Moretó, Alexander, Navarro, Gabriel, Sanus, Lucia, Tiep, Pham Huu

We give a characterization of the finite groups having nilpotent or abelian Hall $\pi$-subgroups which can easily be verified from the character table.

Externí odkaz: http://arxiv.org/abs/1310.8413

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Products of conjugacy classes in finite and algebraic simple groups

Autor: Guralnick, Robert M., Malle, Gunter, Tiep, Pham Huu

We prove the Arad-Herzog conjecture for various families of finite simple groups- if A and B are nontrivial conjugacy classes, then AB is not a conjugacy class. We also prove that if G is a finite simple group of Lie type and A and B are nontrivial c

Externí odkaz: http://arxiv.org/abs/1202.2627

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Character degree sums in finite nonsolvable groups

Autor: Magaard, Kay, Tong-Viet, Hung P.

Let N be a minimal normal nonabelian subgroup of a finite group G. We will show that there exists a nontrivial irreducible character of N of degree at least 5 which is extendible to G. This result will be used to settle two open questions raised by B

Externí odkaz: http://arxiv.org/abs/0912.0875

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