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Let $G$ be a finite group and $π_{e} (G)$ be the set of element orders of $G$ . Let $k \in π_{e} (G)$ and $m_{k}$ be the number of elements of order $k$ in $G$ . Set $nse (G) : = {m_{k} : k \in π_{e} (G)}$ . In fact $nse (G)$ is the set of sizes of elements with the same order in $G$ . In this paper, by $nse (G)$ and order, we give a new characterization of finite projective special linear groups $L_{2} (p)$ over a field with $p$ elements, where $p$ is prime. We prove the following theorem: If $G$ is a group such that $| G | = | L_{2} (p) |$ and $nse (G)$ consists of $1$ , $p^{2} - 1$ , $p (p + ϵ) / 2$ and some numbers divisible by $2 p$ , where $p$ is a prime greater than...

A characterization of the simple group ${PSL}_{5} (5)$ by the set of its element orders.

Darafsheh, Mohammad Reza, Sadrudini, Abdollah (2008)

Sibirskij Matematicheskij Zhurnal

A characterization property of the simple group ${PSL}_{4} (5)$ by the set of its element orders

Mohammad Reza Darafsheh, Yaghoub Farjami, Abdollah Sadrudini (2007)

Archivum Mathematicum

Let $ω (G)$ denote the set of element orders of a finite group $G$ . If $H$ is a finite non-abelian simple group and $ω (H) = ω (G)$ implies $G$ contains a unique non-abelian composition factor isomorphic to $H$ , then $G$ is called quasirecognizable by the set of its element orders. In this paper we will prove that the group $P S L_{4} (5)$ is quasirecognizable.

A constructive Approach to Noether's Problem.

Gregor Kemper (1996)

Manuscripta mathematica

A note on Harish-Chandra induction.

Meinholf Geck (1993)

Manuscripta mathematica

A number theoretic approach to Sylow r-subgroups of classical groups.

Mashhour I. AlAli, Christoph Hering, Anni Neumann (2005)

Revista Matemática Complutense

The purpose of this paper is to give a general and a simple approach to describe the Sylow r-subgroups of classical groups.

A problem of Kollár and Larsen on finite linear groups and crepant resolutions

Robert Guralnick, Pham Tiep (2012)

Journal of the European Mathematical Society

The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age $\leq 1$ . More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation. As a consequence...

A rank 3 tangent complex of ${PSp}_{4} (q)$ , $q$ odd.

Sarli, John, McClurg, Phillip (2001)

Advances in Geometry

A Specialization Theorem for Certain Weyl Group Representations and an Application to the Green Polynomials of Unitary Groups.

R. Hotta, T.A. Springer (1977)

Inventiones mathematicae

A transvection decomposition in GL(n,2)

Clorinda De Vivo, Claudia Metelli (2002)

Colloquium Mathematicae

An algorithm is given to decompose an automorphism of a finite vector space over ℤ₂ into a product of transvections. The procedure uses partitions of the indexing set of a redundant base. With respect to tents, i.e. finite ℤ₂-representations generated by a redundant base, this is a decomposition into base changes.

Abstract homomorphisms of simple algebraic groups

Robert Steinberg (1972/1973)

Séminaire Bourbaki

Algebraic zip data.

Pink, Richard, Wedhorn, Torsten (2011)

Documenta Mathematica

An implementation of the Neumann-Praeger algorithm for the recognition of special linear groups.

Holt, Derek F., Rees, Sarah (1992)

Experimental Mathematics

Automorphic realization of residual Galois representations

Robert Guralnick, Michael Harris, Nicholas M. Katz (2010)

Journal of the European Mathematical Society

We show that it is possible in rather general situations to obtain a finite-dimensional modular representation $ρ$ of the Galois group of a number field $F$ as a constituent of one of the modular Galois representations attached to automorphic representations of a general linear group over $F$ , provided one works “potentially.” The proof is based on a close study of the monodromy of the Dwork family of Calabi–Yau hypersurfaces; this in turn makes use of properties of rigid local systems and the classification...

Barnes' identities and representations of GL (2). I. Finite field case.

Wen-Ch'ing Winnie Li, J. Soto-Andrade (1983)

Journal für die reine und angewandte Mathematik

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