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The character degree graph of a finite group $G$ is the graph whose vertices are the prime divisors of the irreducible character degrees of $G$ and two vertices $p$ and $q$ are joined by an edge if $p q$ divides some irreducible character degree of $G$ . It is proved that some simple groups are uniquely determined by their orders and their character degree graphs. But since the character degree graphs of the characteristically simple groups are complete, there are very narrow class of characteristically simple...

Recognition of some families of finite simple groups by order and set of orders of vanishing elements

Maryam Khatami, Azam Babai (2018)

Czechoslovak Mathematical Journal

Let $G$ be a finite group. An element $g \in G$ is called a vanishing element if there exists an irreducible complex character $χ$ of $G$ such that $χ (g) = 0$ . Denote by $Vo (G)$ the set of orders of vanishing elements of $G$ . Ghasemabadi, Iranmanesh, Mavadatpour (2015), in their paper presented the following conjecture: Let $G$ be a finite group and $M$ a finite nonabelian simple group such that $Vo (G) = Vo (M)$ and $| G | = | M |$ . Then $G ≅ M$ . We answer in affirmative this conjecture for $M = S z (q)$ , where $q = 2^{2 n + 1}$ and either $q - 1$ , $q - \sqrt{2 q} + 1$ or $q + \sqrt{2 q} + 1$ is a prime number, and $M = F_{4} (q)$ , where $q = 2^{n}$ and either...

Recognition of some linear groups over the binary field by the spectrum.

Lucido, Maria Silvia, Moghaddamfar, Ali Reza (2006)

Sibirskij Matematicheskij Zhurnal

Recognition of the finite simple groups $F_{4} (2^{m})$ by the spectrum.

Cao, H.P., Chen, Guiyun, Grechkoseeva, M.A., Mazurov, V.D., Shi, W.J., Vasil'ev, A.V. (2004)

Sibirskij Matematicheskij Zhurnal

Recognition of the group $O_{10}^{+} (2)$ from its spectrum.

Grechkoseeva, M. A. (2003)

Sibirskij Matematicheskij Zhurnal

Recognizability by spectrum of the group $L_{2} (7)$ in the class of all groups.

Lytkina, D.V., Kuznetsov, A.A. (2007)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

Recognizability of finite groups by Suzuki group

Alireza Khalili Asboei, Seyed Sadegh Salehi Amiri (2019)

Archivum Mathematicum

Let $G$ be a finite group. The main supergraph $𝒮 (G)$ is a graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $o (x) ∣ o (y)$ or $o (y) ∣ o (x)$ . In this paper, we will show that $G ≅ S z (q)$ if and only if $𝒮 (G) ≅ 𝒮 (S z (q))$ , where $q = 2^{2 m + 1} \geq 8$ .

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Displaying 1 – 20 of 22

Rank analogues of Hall's and Baer's theorems.

Rank three residually connected geometries for $M_{22}$ , revisited.

Rational Lie Algebras and p-Isomorphisms of Nilpotent Groups and Homotopy Types.

Rational Representations of Finite Groups and Their Euler Class.

Realisierung endlicher Gruppen als Galoisgruppen.

Recognition by the set of element orders of symmetric groups of degree $r$ and $r + 1$ for prime $r$ .

Recognition of alternating groups of prime degree from their element orders.

Recognition of characteristically simple group $A_{5} \times A_{5}$ by character degree graph and order

Recognition of some families of finite simple groups by order and set of orders of vanishing elements

Recognition of some linear groups over the binary field by the spectrum.

Recognition of the finite simple groups $F_{4} (2^{m})$ by the spectrum.

Recognition of the group $O_{10}^{+} (2)$ from its spectrum.

Recognizability by spectrum of the group $L_{2} (7)$ in the class of all groups.

Recognizability of finite groups by Suzuki group

Rectificatif à l'article «Présentation de certains couples fischériens de type classique»

Regular Orbits fo Hall ...-subgroups.

Relative Relation Modules as Generators for Integral Group Rings of Finite Groups.

Remark on the multiplicity of a partition of a group into cosets

Representation of odd integers as the sum of one prime, two squares of primes and powers of 2

Representations of automorphisms on differentials of function fields of characteristic p.

Currently displaying 1 – 20 of 22