Zobrazeno 1 - 10
of 461
pro vyhledávání: '"20d05"'
Autor:
Sabatini, Luca
Let $G$ be a permutation group on the finite set $\Omega$. We study partitions of $\Omega$ whose stabilizers have bounded derived length, proving the following three theorems. In every solvable permutation group, there is a subset whose setwise stabi
Externí odkaz:
http://arxiv.org/abs/2411.18534
Autor:
van Beek, Martin
We determine all reduced saturated fusion systems supported on a finite $p$-group of nilpotency class two. As a consequence, we obtain a new proof of Gilman & Gorenstein's classification of finite simple groups with class two Sylow $2$-subgroups.
Externí odkaz:
http://arxiv.org/abs/2409.18870
In this article, we determine the non-real elements--the ones that are not conjugate to their inverses--in the group $G = G_2(q)$ when $char(F_q)\neq 2,3$. We use this to show that this group is chiral; that is, there is a word w such that $w(G)\neq
Externí odkaz:
http://arxiv.org/abs/2408.15546
We prove that if $G$ is a finite simple group and $x, y \in G$ are involutions, then $|x^G \cap C_G(y)| \rightarrow \infty$ as $|G| \rightarrow \infty$. This extends results of Guralnick-Robinson and Skresanov. We also prove a related result about $C
Externí odkaz:
http://arxiv.org/abs/2407.16926
Autor:
Tong-Viet, Hung P.
For a finite group $G$ and an irreducible complex character $\chi$ of $G$, the codegree of $\chi$ is defined by $\textrm{cod}(\chi)=|G:\textrm{ker}(\chi)|/\chi(1)$, where $\textrm{ker}(\chi)$ is the kernel of $\chi$. In this paper, we show that if $H
Externí odkaz:
http://arxiv.org/abs/2406.17794
Autor:
Brooks, Thomas G.
Julius Whiston calculated the maximum size of an irredundant generating set for $S_n$ and $A_n$ by examination of maximal subgroups. Using analogous considerations, we will compute upper bounds to this value for the first two Mathieu groups, $M_{11}$
Externí odkaz:
http://arxiv.org/abs/2404.17995
Autor:
Tong-Viet, Hung P.
Publikováno v:
Pacific J. Math. 329 (2024) 303-325
Let $G$ be a finite group and let $H$ be a subgroup of $G$. We say that $H$ is extremely closed in $G$ if $\langle H,H^g\rangle\cap N_G(H)=H$ for all $g\in G.$ In this paper, we determine the structure of finite groups with an extremely closed abelia
Externí odkaz:
http://arxiv.org/abs/2404.06307
Autor:
Skresanov, Saveliy V.
The famous Brauer-Fowler theorem states that the order of a finite simple group can be bounded in terms of the order of the centralizer of an involution. Using the classification of finite simple groups, we generalize this theorem and prove that if a
Externí odkaz:
http://arxiv.org/abs/2402.05437
Autor:
Dastborhan, Nasrin, Mousavi, Hamid
Let $\mathfrak{Nil}$ be the class of nilpotent groups and $G$ be a group. We call $G$ a meta-$\mathfrak{Nil}$-Hamiltonian group if any of its non-$\mathfrak{Nil}$ subgroups is normal. Also, we call $G$ a para-$\mathfrak{Nil}$-Hamiltonian group if $G$
Externí odkaz:
http://arxiv.org/abs/2311.00352
Autor:
Shi, Wujie
Publikováno v:
The original version of this article was published in Chinese in the journal Scientia Sinica Mathematica, no.53(2023), pp.931-952. This revised and expanded version has corrected several errors and added quite a few contents
In this paper, we summarize the work on the characterization of finite simple groups and the study on finite groups with the set of element orders and two orders (the order of group and the set of element orders). Some related topics, and the applica
Externí odkaz:
http://arxiv.org/abs/2309.06362