Zobrazeno 1 - 10
of 41
pro vyhledávání: '"Vdovin, Evgeny P."'
Publikováno v:
Mat. Sb., 214:1 (2023), 113-154
Let $\pi$ be a set of primes such that $|\pi|\geqslant 2$ and $\pi$ differs from the set of all primes. Denote by $r$ the smallest prime which does not belong to $\pi$ and set $m=r$ if $r=2,3$ and $m=r-1$ if $r\geqslant 5$. We study the following con
Externí odkaz:
http://arxiv.org/abs/2105.02442
In this paper we show that if S is a simple classical group, a group G is contained in inner-diagonal automorphisms of S and contains S, and H is a solvable Hall subgroup of G, then there exists five conjugates of H, whose intersection is trivial.
Externí odkaz:
http://arxiv.org/abs/2101.04542
Publikováno v:
Israel Journal of Mathematics 2021
In the paper we prove (modulo the classification of finite simple groups) an analogue of the famous Baer-Suzuki theorem for the $\pi$-radical of a finite group, where $\pi$ is a set of primes
Externí odkaz:
http://arxiv.org/abs/1911.11939
Let $\mathfrak{X}$ be a class of finite groups closed under taking subgroups, homomorphic images and extensions. It is known that if $A$ is a normal subgroup of a finite group $G$ then the image of an $\mathfrak{X}$-maximal subgroup $H$ of $G$ in $G/
Externí odkaz:
http://arxiv.org/abs/1808.10107
Publikováno v:
Sb. Math., 211:3 (2020), 309--335
Let $\pi$ be a set of primes. We say that a finite group $G$ is a $\mathcal{D}_\pi$-group if the maximal $\pi$-subgroups of $G$ are conjugate. In this paper, we give an affirmative answer to Problem 17.44(b) from "Kourovka notebook", namely we prove
Externí odkaz:
http://arxiv.org/abs/1808.03536
Publikováno v:
Journal of Group Theory, 22 (2019) 713-728
In the paper we consider images of finite simple projective special linear and unitary groups under power words. In particular, we show that if $G\simeq \PSL_n^\varepsilon (q)$, then for every power words of type $x^M$ there exist constant $c$ and $N
Externí odkaz:
http://arxiv.org/abs/1805.04638
Autor:
Guo, Wenbin, Vdovin, Evgeny
Denote by $\nu_p(G)$ the number of Sylow $p$-subgroups of $G$. It is not difficult to see that $\nu_p(H)\leq\nu_p(G)$ for $H\leq G$, however $\nu_p(H)$ does not divide $\nu_p(G)$ in general. In this paper we reduce the question whether $\nu_p(H)$ div
Externí odkaz:
http://arxiv.org/abs/1709.00148
Suppose that a finite solvable group $G$ acts faithfully, irreducibly and quasi-primitively on a finite vector space $V$. Then $G$ has a uniquely determined normal subgroup $E$ which is a direct product of extraspecial $p$-groups for various $p$ and
Externí odkaz:
http://arxiv.org/abs/1612.05959
Let $\pi$ be a set of primes. By H.Wielandt definition, {\it Sylow $\pi$-theorem} holds for a finite group $G$ if all maximal $\pi$-subgroups of $G$ are conjugate. In the paper, the following statement is proven. Assume that $\pi$ is a union of disjo
Externí odkaz:
http://arxiv.org/abs/1407.2007
Autor:
Revin, Danila, Vdovin, Evgeny
In the paper, it is proved that if a finite group $G$ possesses a $\pi$-Hall subgroup for a set $\pi$ of primes, then every normal subgroup $A$ of $G$ possesses a $\pi$-Hall subgroup $H$ such that ${G=AN_G(H)}$.
Externí odkaz:
http://arxiv.org/abs/1401.7719