Tootfinder

This https://arxiv.org/abs/2202.10812 has been replaced.
link: https://scholar.google.com/scholar?q=a

Anti-associative algebras
An anti-associative algebra is a nonassociative algebra whose multiplication satisfies the identity a(bc)+(ab)c=0. Such algebras are nilpotent. We describe the free anti-associative algebras with a finite number of generators. Other types of nonassociative algebras, obtained either by the process of polarization, such as Jacobi-Jordan algebras, or obtained by deformation quantization, are associated with this class of algebras. Following Markl-Remms work, we describe the operads associated with…

A note on the $ \Pi $-property of some subgroups of finite groups
Zhengtian Qiu, Jianjun Liu, Guiyun Chen
https://arxiv.org/abs/2405.05106 https://<…

A note on the $ Π$-property of some subgroups of finite groups
Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the $ Π$-property in $ G $ if for any chief factor $ L / K $ of $ G $, $ |G/K : N_{G/K}(HK/K\cap L/K )| $ is a $ π(HK/K\cap L/K) $-number. In this paper, we obtain some criteria for the $ p $-supersolubility or $ p $-nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the $ Π$-property.

This https://arxiv.org/abs/2402.01189 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Malle's conjecture for the product of symmetric and nilpotent groups
Let $G$ be a finite nilpotent group and $n\in \{3,4, 5\}$. Consider $S_n\times G$ as a subgroup of $S_n\times S_{|G|}\subset S_{n|G|}$, where $G$ embeds into the second factor of $S_n\times S_{|G|}$ via the regular representation. Over any number field $k$, we prove the strong form of Malle's conjecture for $S_n\times G$ viewed as a subgroup of $S_{n|G|}$. Our result requires that $G$ satisfies some mild conditions.

Omega-categorical pseudofinite groups
Dugald Macpherson, Katrin Tent
https://arxiv.org/abs/2403.17684 https://arxiv.org/pdf/2403.1768…

Omega-categorical pseudofinite groups
We explore the interplay between omega-categoricity and pseudofiniteness for groups, conjecturing that omega-categorical pseudofinite groups are finite-by-abelian-by-finite. We show that the conjecture reduces to nilpotent p-groups of class 2, and give a proof that several of the known examples of omega-categorical p-groups satisfy the conjecture. In particular, we show by a direct counting argument that for any odd prime p the (omega-categorical) model companion of the theory of nilpotent clas…

p-Nilpotent maximal subgroups in finite groups
Antonio Beltr\'an, Changguo Shao
https://arxiv.org/abs/2402.18413 https://arxiv.or…

p-Nilpotent maximal subgroups in finite groups
Let $G$ be a finite group, $p$ a prime, and suppose that every maximal subgroup of $G$ is $p$-nilpotent or has prime index in $G$. We prove, relying in the Classification of Finite Simple Groups, that if $p$ is odd and $p\neq 5$, then $G$ is $p$-solvable, and the $p$-length of $G$ is at most $2$. For $p=5$, however, a group $G$ satisfying the same conditions need not be $5$-solvable, and in that case we show that $G/S_5(G)\cong{\rm PSL}_2(11)$, where $S_5(G)$ is the $5$-solvable radical of $G$.…

This https://arxiv.org/abs/2212.07930 has been replaced.
link: https://scholar.google.com/scholar?q=a

Singular contact varieties
In this note we propose the generalization of the notion of a holomorphic contact structure on a manifold (smooth variety) to varieties with rational singularities and prove basic properties of such objects. Natural examples of singular contact varieties come from the theory of nilpotent orbits: every projectivization of the closure of a nilpotent orbit in a semisimple Lie algebra satisfies our definition after normalization. We show the correspondence between symplectic varieties with the stru…