Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Revin, Danila O."'
As defined by Guralnick and Saxl given a nonabelian simple group $S$ and its nonidentity automorphism $x$, a natural number $\alpha_S(x)$ does not exceed a natural number $m$ if some $m$ conjugates of $x$ in the group $\langle x,S\rangle$ generate a
Externí odkaz:
http://arxiv.org/abs/2402.03673
We prove that if $L=\mbox{}^2F_4(2^{2n+1})'$ and $x$ is a nonidentity automorphism of $L$ then $G=\langle L,x\rangle$ has four elements conjugate to $x$ that generate $G$. This result is used to study the following conjecture about the $\pi$-radical
Externí odkaz:
http://arxiv.org/abs/2212.13785
Publikováno v:
Archiv der Mathematik (Basel), 121, no. 1 (2023), 11--21
Let $\mathfrak{X}$ be a class of finite groups closed under subgroups, homomorphic images, and extensions. We study the question which goes back to the lectures of H. Wielandt in 1963-64: For a given $\mathfrak{X}$-subgroup $K$ and maximal $\mathfrak
Externí odkaz:
http://arxiv.org/abs/2206.10267
Publikováno v:
In Journal of Pure and Applied Algebra December 2024 228(12)
Publikováno v:
Sib. Math. J. 63, 387-394 (2022)
Let $\pi$ be a proper subset of the set of all primes. Denote by $r$ the smallest prime which does not belong to $\pi$ and set $m = r$ if $r = 2$ or $3$ and $m = r-1$ if $r \geqslant 5$. We study the following conjecture: a conjugacy class $D$ of a f
Externí odkaz:
http://arxiv.org/abs/2111.09066
Autor:
Guo, Wenbin, Revin, Danila O.
Publikováno v:
Ser. Mat., 86:6 (2022), 79-100
Let ${\mathfrak{X}}$ be a class of finite groups closed under taking subgroups, homomorphic images, and extensions. Denote by ${\mathrm{k}}_{\mathfrak{X}}(G)$ the number of conjugacy classes ${\mathfrak{X}}$-maximal subgroups of a finite group $G$. T
Externí odkaz:
http://arxiv.org/abs/2110.15638
Let a group $A$ act on the group $G$ coprimely. Suppose that the order of the fixed point subgroup $C_G(A)$ is not divisible by an arbitrary but fixed prime $p$. In the present paper we determine bounds for the $p$-length of the group $G$ in terms of
Externí odkaz:
http://arxiv.org/abs/2105.10807
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
Publikováno v:
Journal of Group Theory, 2021
We complete the description of automorphism groups of all nonsplit extensions of elementary abelian $2$-groups by $PSL_2(q)$, with $q$ odd, for an irreducible induced action. An application of this result to the theory of $\pi$-submaximal subgroups i
Externí odkaz:
http://arxiv.org/abs/2104.09201
Publikováno v:
Sib. Elect. Math. Reports, V.17 (2020), 1155--1164
We explore the extent to which constructing the inductive theory of $\mathfrak{X}$-submaximal subgroups is possible. To this end, we study the behavior of $\pi$-submaximal subgroups under homomorphisms with $\pi$-separable kernels and construct examp
Externí odkaz:
http://arxiv.org/abs/2006.09752