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Product decompositions of quasirandom groups and a Jordan type theorem

Nikolay Nikolov, László Pyber (2011)

Journal of the European Mathematical Society

We first note that a result of Gowers on product-free sets in groups has an unexpected consequence: If $k$ is the minimal degree of a representation of the finite group $G$ , then for every subset $B$ of $G$ with $| B | > | G | / k^{1 / 3}$ we have $B^{3} = G$ . We use this to obtain improved versions of recent deep theorems of Helfgott and of Shalev concerning product decompositions of finite simple groups, with much simpler proofs. On the other hand, we prove a version of Jordan’s theorem which implies that if $k \geq 2$ , then $G$ has a proper subgroup...

Properties of element orders in covers for $L_{n} (q)$ and $U_{n} (q)$ .

Zavarnitsine, A.V. (2008)

Sibirskij Matematicheskij Zhurnal

Quand seule la sous-somme vide est nulle modulo $p$

Jean-Marc Deshouillers (2007)

Journal de Théorie des Nombres de Bordeaux

Soit $c > 1$ , $p$ un nombre premier et $𝒜$ une partie de $ℤ / p ℤ$ de cardinal supérieur à $c \sqrt{p}$ telle que pour tout sous-ensemble non vide $ℬ$ de $𝒜$ , on a $\sum_{b \in ℬ} b \neq 0$ . On montre qu’il existe $s$ premier à $p$ tel que l’ensemble $s . 𝒜$ est très concentré autour de l’origine et qu’il est presque entièrement composé d’éléments de partie fractionnaire positive. Plus précisément, on a $\sum_{a \in 𝒜} ∥\frac{s a}{p}∥ < 1 + O (p^{- 1 / 4} ln p) et \sum_{\begin{matrix} a \in 𝒜, \\ {s a / p} \geq 1 / 2 \end{matrix}} ∥\frac{s a}{p}∥ = O (p^{- 1 / 4} ln p) .$ On montre également que les termes d’erreurs ne peuvent être remplacés par $o (p^{- 1 / 2})$ .

Quasirecognition by prime graph of $^{2} D_{p} (3)$ where $p = 2^{n} + 1 \geq 5$ is a prime.

Babai, A., Khosravi, B., Hasani, N. (2009)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Quasirecognition by prime graph of $L_{10} (2)$ .

Khosravi, Behrooz (2009)

Sibirskij Matematicheskij Zhurnal

Quasirecognition by prime graph of the simple group $^{2} G_{2} (q)$ .

Khosravi, Amir, Khosravi, Behrooz (2007)

Sibirskij Matematicheskij Zhurnal

Quasirecognition by the set of element orders of the groups $E_{6} (q)$ and $^{2} E_{6} (q)$ .

Kondrat'ev, A.S. (2007)

Sibirskij Matematicheskij Zhurnal

Quasirecognition of a class of finite simple groups by the set of element orders.

Alekseeva, O. A., Kondrat'ev, A. S. (2003)

Sibirskij Matematicheskij Zhurnal

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

Makarenko, N.Yu. (2000)

Sibirskij Matematicheskij Zhurnal

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

Zavarnitsin, A.V. (2002)

Sibirskij Matematicheskij Zhurnal

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

Kondrat'ev, A.S., Mazurov, V.D. (2000)

Siberian Mathematical Journal

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

Maryam Khademi, Behrooz Khosravi (2018)

Czechoslovak Mathematical Journal

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...

Currently displaying 201 – 220 of 319

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Displaying 201 – 220 of 319

Product decompositions of quasirandom groups and a Jordan type theorem

Properties of element orders in covers for $L_{n} (q)$ and $U_{n} (q)$ .

Quand seule la sous-somme vide est nulle modulo $p$

Quasirecognition by prime graph of $^{2} D_{p} (3)$ where $p = 2^{n} + 1 \geq 5$ is a prime.

Quasirecognition by prime graph of $L_{10} (2)$ .

Quasirecognition by prime graph of the simple group $^{2} G_{2} (q)$ .

Quasirecognition by the set of element orders of the groups $E_{6} (q)$ and $^{2} E_{6} (q)$ .

Quasirecognition of a class of finite simple groups by the set of element orders.

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

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 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.

Regular Orbits fo Hall ...-subgroups.

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

Schur multipliers of p-groups.

Currently displaying 201 – 220 of 319