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Unipotent radicals, one-dimensional transitive groups, and solvable factors of classical groups

Autor: Feng, Tao, Li, Cai Heng, Li, Conghui, Wang, Lei, Xia, Binzhou, Zou, Hanlin

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

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Nonexistence of generalized quadrangles admitting a point-primitive and line-primitive automorphism group with socle ${\rm PSU}(3,q)$, $q\geq 3$

Autor: Lu, Jianbing, Zhang, Yingnan, Zou, Hanlin

A central problem in the study of generalized quadrangles is to classify finite generalized quadrangles satisfying certain symmetry conditions. It is known that an automorphism group of a finite thick generalized quadrangle $\mathcal{S}$ acting primi

Externí odkaz: http://arxiv.org/abs/2403.00240

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An infinite family of $m$-ovoids of the hyperbolic quadrics $\mathcal{Q}^+(7,q)$

Autor: Pavese, Francesco, Zou, Hanlin

An infinite family of $(q^2+q+1)$-ovoids of $\mathcal{Q}^+(7,q)$, $q\equiv 1\pmod{3}$, admitting the group $\mathrm{PGL}(3,q)$, is constructed. The main tool is the general theory of generalized hexagons.
Comment: 9 pages

Externí odkaz: http://arxiv.org/abs/2309.06821

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Constructions of tight sets of the Hermitian polar space $\mc{H}(2r-1,q^2)$

Autor: Hui, Alice M. W., Li, Weicong, Xiang, Qing, Zou, Hanlin

In this paper, we construct two infinite families of tight sets with parameters $(q^{2r-2}-1)$ and $(q^{2r-1}-q^{2r-2})$, respectively, in the Hermitian polar space $\mathcal{H}(2r-1,q^2)$ for any $r\ge 2$ and any prime power $q$. Both families admit

Externí odkaz: http://arxiv.org/abs/2112.10097

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Cameron-Liebler Line Classes with parameter $x=\frac{(q+1)^2}{3}$

Autor: Feng, Tao, Momihara, Koji, Rodgers, Morgan, Xiang, Qing, Zou, Hanlin

Publikováno v: Adv. Math. 385 (2021)

Cameron-Liebler line classes were introduced in \cite{CL}, and motivated by a question about orbits of collineation groups of $\PG(3,q)$. These line classes have appeared in different contexts under disguised names such as Boolean degree one function

Externí odkaz: http://arxiv.org/abs/2006.14206

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