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Nilpotent primitive linear groups over finite fields
A. S. Detinko, D. L. Flannery
https://arxiv.org/abs/2507.20628 https://arxiv.org/pdf/2507.20628…

Nilpotent primitive linear groups over finite fields
We provide a detailed structural description of the nilpotent primitive subgroups of $\mathrm{GL}(n, \mathbb{F})$, where $\mathbb{F}$ is a finite field.

The nilpotent graph of a finite0-dimensional Lie algebra
David Towers, Ismael Gutierrez, Luis Fernandez
https://arxiv.org/abs/2506.19758 https://

The nilpotent graph of a finite0-dimensional Lie algebra
Let $L$ be a finite-dimensional Lie algebra over a field $F$. In This paper we introduce the \emph{nilpotent graph} $Γ_\mathfrak{N}(L)$ as the graph whose vertices are the elements of $L \setminus \nil(L)$, where \[\nil(L) = \{x \in L \mid \langle x, y \rangle \text{ is nilpotent for all } y \in L\},\] and where two vertices $x, y$ are adjacent if the Lie subalgebra they generate is nilpotent. We give some characterizations of $\nil(L)$ and its connection with the hypercenter $Z^*(L)$, for exa…

"Also back in style is the tactic of using disinformation to manufacture consent for war, as with Netanyahu’s claims that Iran was right on the cusp of acquiring a nuclear weapon and intending to supply one to Yemen’s Ansarallah. We are entering territory so fantastical that the ‘dodgy dossier’ and ‘45-minute WMD’ seem almost quaint by comparison."
Eskandar Sadeghi-Boroujerdi, Culmination — Sidecar

Eskandar Sadeghi-Boroujerdi, Culmination — Sidecar
Israel attacks Iran.

#Iran:
"Their solidarity with oppositional forces has been fragmentary and opportunist, devoid of any consistent anti-imperialist strategy, except in their lonely but crucial capacity as a defender of Palestinian rights, in a region where every single Arab government has capitulated to the hegemon."
Tariq Ali, Nuclear Options — Sidecar

Tariq Ali, Nuclear Options — Sidecar
Regime change in Tehran?

This https://arxiv.org/abs/2506.00952 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the class-breadth conjecture
The class-breadth conjecture of Leedham-Green, Neumann and Wiegold states that for each $p$-group, $cl(G)\leq b(G) + 1$, where $cl(G)$, $b(G)$ denote the nilpotency class and the breadth of $G$. While several counter-examples to this conjecture have been found for $p = 2$, it is still open in general for $p > 2$. This article is dedicated to one simplified version of the conjecture for $p > 2$.