Zobrazeno 1 - 10
of 1 308
pro vyhledávání: '"Cai, Heng"'
A positive integer $m$ is called a Hall number if any finite group of order precisely divisible by $m$ has a Hall subgroup of order $m$. We prove that, except for the obvious examples, the three integers $12$, $24$ and $60$ are the only Hall numbers,
Externí odkaz:
http://arxiv.org/abs/2408.03184
By developing a tangible way to decompose unipotent radicals into irreducible submodules of Singer cycles, we achieve a classification of solvable factors of finite classical groups of Lie type. This completes previous work on factorizations of class
Externí odkaz:
http://arxiv.org/abs/2407.12416
Let $G\leqslant\mathrm{Sym}(\Omega)$ be a finite transitive permutation group with point stabiliser $H$. We say that a subgroup $K$ of $G$ is a fixer if every element of $K$ has fixed points, and we say that $K$ is large if $|K| \geqslant |H|$. There
Externí odkaz:
http://arxiv.org/abs/2404.18753
Autor:
Lin, Binbin, Zou, Lei, Yang, Mingzheng, Zhou, Bing, Mandal, Debayan, Abedin, Joynal, Cai, Heng, Ning, Ning
The COVID-19 pandemic has changed human life. To mitigate the pandemic's impacts, different regions implemented various policies to contain COVID-19 and residents showed diverse responses. These human responses in turn shaped the uneven spatial-tempo
Externí odkaz:
http://arxiv.org/abs/2404.10013
A locally-primitive design is a block design $(\mathcal{P},\mathcal{B})$ which admits an automorphism group $G$ with primitive local actions. It is proved that $G$ is primitive on the points $\mathcal{P}$, and either $G$ is an almost simple group, or
Externí odkaz:
http://arxiv.org/abs/2403.16822
Autor:
Li, Cai Heng, Zhu, Yan Zhou
A complete classification is given of finite groups whose elements are partitioned into three orbits by the automorphism groups, solving the long-standing classification problem initiated by G.\,Higman in 1963. As a consequence, a classification is o
Externí odkaz:
http://arxiv.org/abs/2403.01725
We classify the factorizations of finite classical groups with nonsolvable factors, completing the classification of factorizations of finite almost simple groups.
Externí odkaz:
http://arxiv.org/abs/2402.18373
Autor:
Li, Cai Heng, Zhu, Yan Zhou
Building upon previous results, a classification is given of finite $p$-groups of which subgroups of order $p$ are all fused. This completes the classification problem dated back to Higman 1963 on the so-called Suzuki $2$-groups, and confirms a conje
Externí odkaz:
http://arxiv.org/abs/2312.16416
The classification of the finite primitive permutation groups of rank $3$ was completed in the 1980s and this landmark achievement has found a wide range of applications. In the general transitive setting, a classical result of Higman shows that ever
Externí odkaz:
http://arxiv.org/abs/2311.04057