Tootfinder

An exact enumeration of vertex connectivity of the enhanced power graphs of finite nilpotent groups
Sudip Bera, Hiranya Kishore Dey
https://arxiv.org/abs/2405.01027

An exact enumeration of vertex connectivity of the enhanced power graphs of finite nilpotent groups
The enhanced power graph of a group $G$ is a graph with vertex set $G,$ where two distinct vertices $x$ and $y$ are adjacent if and only if there exists an element $w$ in $G$ such that both $x$ and $y$ are powers of $w.$ In this paper, we determine the vertex connectivity of the enhanced power graph of any finite nilpotent group.

This https://arxiv.org/abs/2210.05933 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Whitehead theorem for nilpotent motivic spaces
We improve some foundational connectivity results and the relative Hurewicz theorem in motivic homotopy theory, study functorial central series in motivic local group theory, establish the existence of functorial Moore--Postnikov factorizations for nilpotent morphisms of motivic spaces under a mild technical hypothesis and establish an analog of the Whitehead theorem for nilpotent motivic spaces. As an application, we deduce a surprising unstable motivic periodicity result.

Mekler's Construction and Murphy's Law for 2-Nilpotent Groups
Blaise Boissonneau, Aris Papadopoulos, Pierre Touchard
https://arxiv.org/abs/2403.20270

Mekler's Construction and Murphy's Law for 2-Nilpotent Groups
Mekler's construction is a powerful technique for building purely algebraic structures from combinatorial ones. Its power lies in the fact that it allows various model-theoretic tameness properties of the combinatorial structure to transfer to the algebraic one. In this paper, we push this ideology much further, describing a broad class of properties that transfer through Mekler's construction. This technique subsumes many well-known results and opens avenues for many more. As a straightforwa…

Interesting piece on the relationship of Iran to the Palestinian struggle, and its limits.
Eskandar Sadeghi-Boroujerdi, Rules of the Game — Sidecar https://newleftreview.org/sidecar/posts/rules-of-the-game?pc=1598

Eskandar Sadeghi-Boroujerdi, Rules of the Game — Sidecar
Iran versus Israel.

This https://arxiv.org/abs/2402.07779 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finding product sets in some classes of amenable groups
In 2022, using methods from ergodic theory, Kra, Moreira, Richter, and Robertson resolved a longstanding conjecture of Erdős about sumsets in large subsets of the natural numbers. In this paper, we extend this result to several important classes of amenable groups, including all finitely generated virtually nilpotent groups, and all abelian groups $(G,+)$ with the property that the subgroup $2G := \{g+g : g\in G\}$ has finite index. We prove that in any group $G$ from the above classes, any $A…

Classification of right nilpotent $\mathbb{F}_p$-braces of cardinality $p^5$
Snehashis Mukherjee
https://arxiv.org/abs/2403.14975 https://

Classification of right nilpotent $\mathbb{F}_p$-braces of cardinality $p^5$
In this article the right nilpotent $\mathbb{F}_p$-braces of cardinality $p^5$ has been classified. We use the connection between nilpotent $\mathbb{F}_p$-braces of cardinality $p^5$ and nilpotent pre-Lie algebras of the same order, building on the known relationship between pre-Lie algebras and braces. Leveraging insights from the classification of nilpotent pre-Lie algebras over $\mathbb{F}_p$, we aim to provide a comprehensive classification of right nilpotent $\mathbb{F}_p$-braces of cardin…

Mekler's Construction and Murphy's Law for 2-Nilpotent Groups
Blaise Boissonneau, Aris Papadopoulos, Pierre Touchard
https://arxiv.org/abs/2403.20270

Mekler's Construction and Murphy's Law for 2-Nilpotent Groups
Mekler's construction is a powerful technique for building purely algebraic structures from combinatorial ones. Its power lies in the fact that it allows various model-theoretic tameness properties of the combinatorial structure to transfer to the algebraic one. In this paper, we push this ideology much further, describing a broad class of properties that transfer through Mekler's construction. This technique subsumes many well-known results and opens avenues for many more. As a straightforwa…

Interesting piece on the relationship of Iran to the Palestinian struggle, and its limits.
Eskandar Sadeghi-Boroujerdi, Rules of the Game — Sidecar https://newleftreview.org/sidecar/posts/rules-of-the-game?pc=1598

Eskandar Sadeghi-Boroujerdi, Rules of the Game — Sidecar
Iran versus Israel.

This https://arxiv.org/abs/2402.07779 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finding product sets in some classes of amenable groups
In 2022, using methods from ergodic theory, Kra, Moreira, Richter, and Robertson resolved a longstanding conjecture of Erdős about sumsets in large subsets of the natural numbers. In this paper, we extend this result to several important classes of amenable groups, including all finitely generated virtually nilpotent groups, and all abelian groups $(G,+)$ with the property that the subgroup $2G := \{g+g : g\in G\}$ has finite index. We prove that in any group $G$ from the above classes, any $A…

A Proof of the Box Conjecture for Commuting Pairs of Matrices
J. Irving, T. Ko\v{s}ir, M. Mastnak
https://arxiv.org/abs/2403.18574 https://

A Proof of the Box Conjecture for Commuting Pairs of Matrices
We prove the Box Conjecture for pairs of commuting nilpotent matrices, as formulated by Iarrobino et al \cite{IKvSZ}. This describes the Jordan type of the dense orbit in the nilpotent commutator of a given nilpotent matrix. Our main tool is the Burge correspondence between the set of all partitions and a set of binary words \cite{Bur-1, Bur-2}. For connection with the algebraic and geometric setup of matrices and orbits we employ some of Shayman's results on invariant subspaces of a nilpotent …