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Displaying 21 – 40 of 66

Characterization of the alternating groups by their order and one conjugacy class length

Alireza Khalili Asboei, Reza Mohammadyari (2016)

Czechoslovak Mathematical Journal

Let $G$ be a finite group, and let $N (G)$ be the set of conjugacy class sizes of $G$ . By Thompson’s conjecture, if $L$ is a finite non-abelian simple group, $G$ is a finite group with a trivial center, and $N (G) = N (L)$ , then $L$ and $G$ are isomorphic. Recently, Chen et al. contributed interestingly to Thompson’s conjecture under a weak condition. They only used the group order and one or two special conjugacy class sizes of simple groups and characterized successfully sporadic simple groups (see Li’s PhD dissertation). In...

Characterization of the soluble one-generator totally saturated formations of finite groups.

Safonov, V.G. (2007)

Sibirskij Matematicheskij Zhurnal

Characterizing finite groups whose enhanced power graphs have universal vertices

David G. Costanzo, Mark L. Lewis, Stefano Schmidt, Eyob Tsegaye, Gabe Udell (2024)

Czechoslovak Mathematical Journal

Let $G$ be a finite group and construct a graph $Δ (G)$ by taking $G ∖ {1}$ as the vertex set of $Δ (G)$ and by drawing an edge between two vertices $x$ and $y$ if $〈 x, y 〉$ is cyclic. Let $K (G)$ be the set consisting of the universal vertices of $Δ (G)$ along the identity element. For a solvable group $G$ , we present a necessary and sufficient condition for $K (G)$ to be nontrivial. We also develop a connection between $Δ (G)$ and $K (G)$ when $| G |$ is divisible by two distinct primes and the diameter of $Δ (G)$ is 2.

Characterizing the Sporadic Simple Group of Suzuki by a 2-Local Subgroup.

Hiroyoshi Yamaki (1976)

Mathematische Zeitschrift

Characters and systems of subgroups.

Karl Kronstein (1966)

Journal für die reine und angewandte Mathematik

Characters and the generalized Fitting subgroup

Gabriel Navarro (1988)

Rendiconti del Seminario Matematico della Università di Padova

Characters of finite groups and divisibility problems. (Charaktere endlicher Gruppen und Teilbarkeitsfragen.)

Kerber, Adalbert (1981)

Séminaire Lotharingien de Combinatoire [electronic only]

Characters of Groups with Normal Extra Special Subgroups.

Everett C. Dade (1976/1977)

Mathematische Zeitschrift

Charaktere endlicher Gruppen mit vorgegebenen Schurschen Indizes.

Falko Lorenz (1971)

Mathematische Annalen

Charakterisierungen einiger Schunckklassen endlicher auflösbarer Gruppen II.

Peter Förster (1978)

Mathematische Zeitschrift

Chern Classes and Extraspecial Groups.

David J. Green, Ian J. Leary (1995)

Manuscripta mathematica

Classification of finite groups satisfying a minimal condition.

Li, Shirong, Meng, Wei (2009)

Sibirskij Matematicheskij Zhurnal

Classification of finite groups with many minimal subgroups and with the number of conjugacy classes of G/S(G) equal to 8.

Antonio Vera López, Jesús María Arregi Lizarraga, Francisco José Vera López (1990)

Collectanea Mathematica

In this paper we classify all the finite groups satisfying r(G/S(G))=8 and ß(G)=r(G) - a(G) - 1, where r(G) is the number of conjugacy classes of G, ß(G) is the number of minimal normal subgroups of G, S(G) the socle of G and a(G) the number of conjugacy classes of G out of S(G). These results are a contribution to the general problem of the classification of the finite groups according to the number of conjugacy classes.

Classification of solvable groups possessing a unique nonlinear non-faithful irreducible character

Amin Saeidi (2014)

Open Mathematics

In this note, we study finite groups possessing exactly one nonlinear non-faithful irreducible character. Our main result is to classify solvable groups that satisfy this property. Also, we give examples to show that these groups need not to be solvable in general.

Currently displaying 21 – 40 of 66

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Displaying 21 – 40 of 66

Characterization of the alternating groups by their order and one conjugacy class length

Characterization of the soluble one-generator totally saturated formations of finite groups.

Characterizing finite groups whose enhanced power graphs have universal vertices

Characterizing the Sporadic Simple Group of Suzuki by a 2-Local Subgroup.

Characters and systems of subgroups.

Characters and the generalized Fitting subgroup

Characters of finite groups and divisibility problems. (Charaktere endlicher Gruppen und Teilbarkeitsfragen.)

Characters of Groups with Normal Extra Special Subgroups.

Charaktere endlicher Gruppen mit vorgegebenen Schurschen Indizes.

Charakterisierungen einiger Schunckklassen endlicher auflösbarer Gruppen II.

Chern Classes and Extraspecial Groups.

Classification of finite groups satisfying a minimal condition.

Classification of finite groups with many minimal subgroups and with the number of conjugacy classes of G/S(G) equal to 8.

Classification of solvable groups possessing a unique nonlinear non-faithful irreducible character

Classifying spectra of saturated fusion systems.

Cliques of irreducible representations of p-solvable groups and a theorem analogous to Alperin's conjecture.

Closure Properties for Fitting Functors.

CLT and non-CLT groups of order $p^{2} q^{2}$

Cohomological characterisations of saturated formations and homomorphs of finite groups.

Collineation Groups of Finite Projective Planes Whose Sylow 2-Subgroups Contain at most Three Involutions.

Currently displaying 21 – 40 of 66