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On $A$-Groups with the Same Index Set as a Nilpotent Group
Wei Zhou, Ilya Gorshkov
https://arxiv.org/abs/2506.15250 https://arxiv.org…

On $A$-Groups with the Same Index Set as a Nilpotent Group
Let $G$ be a finite group and $N(G)$ be the set of conjugacy class sizes of $G$. For a prime $p$, let $|G||_p$ be the highest $p$-power dividing some element of $N(G)$. and define $|G|| = Π_{p\in π(G)}|G||_p$. $G$ is said to be an $A$-group if all its Sylow subgroups are abelian. We prove that if $G$ is an $A$-group such that $N(G)$ contains $|G||_p$ for every $p\in π(G)$ as well as $|G||$, then $G$ must be abelian. T…

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p-K\"ahler structures on compact complex manifolds
Ettore Lo Giudice
https://arxiv.org/abs/2506.13546 https://arxiv.org/pdf/2506…

p-Kähler structures on compact complex manifolds
Let $(M,J)$ be a complex manifold of complex dimension $n$. A $p$-Kähler structure on $(M,J)$ is a real, closed $(p,p)$-transverse form. In this paper, we address the conjecture of L. Alessandrini and G. Bassanelli on $(n-2)$-Kähler nilmanifolds equipped with nilpotent complex structures and holomorphically parallelizable nilmanifolds. We also derive necessary conditions for the existence of smooth curves of $p$-Kähler structures, starting from a fixed $p$-Kähler structure, along a differen…

The geometric classification of nilpotent Lie-Yamaguti, Bol and compatible Lie algebras
Kobiljon Abdurasulov, Abror Khudoyberdiyev, Feruza Toshtemirova
https://arxiv.org/abs/2506.05353

The geometric classification of nilpotent Lie-Yamaguti, Bol and compatible Lie algebras
The geometric classifications of complex $4$-dimensional nilpotent Lie-Yamaguti algebras, $4$-dimensional nilpotent Bol algebras, and $4$-dimensional nilpotent compatible Lie algebras are given.

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Imprint of $\alpha$-clustering on nucleon-nucleon correlations in relativistic light ion collisions
Hadi Mehrabpour
https://arxiv.org/abs/2506.12673 https:…

Imprint of $α$-clustering on nucleon-nucleon correlations in relativistic light ion collisions
This study investigates the influence of $α$-cluster structures in relativistic light nuclear collisions. Using a cluster framework, the characteristics of the nucleonic configurations of $^{16}$ O and $^{20}$ Ne are extracted as predicted by various \textit{ab initio} models, including Nuclear Lattice Effective Field Theory (NLEFT), Variational Monte Carlo (VMC), and the Projected Generator Coordinate Method (PGCM). Additionally, I analyze configurations derived from a three-parameter Fermi (…

Expanding Ricci solitons and Higgs bundles
Ramiro A. Lafuente, Adam Thompson
https://arxiv.org/abs/2506.11362 https://arxiv.org/pdf/2…

Expanding Ricci solitons and Higgs bundles
Motivated by the long-time behavior of Ricci flows that collapse with bounded curvature, we study expanding Ricci solitons with nilpotent symmetry on vector bundles over a closed manifold. We prove that, under mild assumptions that are satisfied by Ricci flow limits, the equations dimension-reduce to the so-called twisted harmonic-Einstein equations. When the base is a surface, we establish a correspondence between solutions of the latter and a class of G-Higgs bundles. This allows us to produc…

This https://arxiv.org/abs/2506.02885 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On an extension of Shlyk's theorem
In this paper, we prove that the intersection of all non-nilpotent maximal subgroups of a non-solvable group containing the normalizer of some Sylow subgroup is nilpotent, which provides an extension of Shlyk's theorem.

Nilpotent graphs over skew PBW extensions
Sebasti\'an Higuera, Armando Reyes
https://arxiv.org/abs/2506.00632 https://arxiv.org/p…

Nilpotent graphs over skew PBW extensions
We investigate the diameter and girth of the nilpotent graph for skew PBW extensions over $2$-primal rings, generalizing similar results on skew polynomial rings. Under certain compatibility conditions, we establish bounds for the diameter of the nilpotent graph and prove invariance of the girth under polynomial extensions.

On an extension of Shlyk's theorem
Jiangtao Shi, Fanjie Xu, Na Li
https://arxiv.org/abs/2506.02885 https://arxiv.org/pdf/2506.028…

On an extension of Shlyk's theorem
In this paper, we prove that the intersection of all non-nilpotent maximal subgroups of a non-solvable group containing the normalizer of some Sylow subgroup is nilpotent, which provides an extension of Shlyk's theorem.