Torsion units for some almost simple groups

Joe Gildea

Displaying similar documents to “Torsion units for some almost simple groups”

The cuspidal torsion packet on hyperelliptic Fermat quotients

David Grant, Delphy Shaulis (2004)

Journal de Théorie des Nombres de Bordeaux

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Let $ℓ \geq 7$ be a prime, $C$ be the non-singular projective curve defined over $ℚ$ by the affine model $y (1 - y) = x^{ℓ}$ , $\infty$ the point of $C$ at infinity on this model, $J$ the Jacobian of $C$ , and $φ : C \to J$ the albanese embedding with $\infty$ as base point. Let $\bar{ℚ}$ be an algebraic closure of $ℚ$ . Taking care of a case not covered in [], we show that $φ (C) \cap J_{tors} (\bar{ℚ})$ consists only of the image under $φ$ of the Weierstrass points of $C$ and the points $(x, y) = (0, 0)$ and $(0, 1)$ , where $J_{tors}$ denotes the torsion points of $J$ .

Torsion points in families of Drinfeld modules

Dragos Ghioca, Liang-Chung Hsia (2013)

Acta Arithmetica

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Let $Φ^{λ}$ be an algebraic family of Drinfeld modules defined over a field K of characteristic p, and let a,b ∈ K[λ]. Assume that neither a(λ) nor b(λ) is a torsion point for $Φ^{λ}$ for all λ. If there exist infinitely many λ ∈ K̅ such that both a(λ) and b(λ) are torsion points for $Φ^{λ}$ , then we show that for each λ ∈ K̅, a(λ) is torsion for $Φ^{λ}$ if and only if b(λ) is torsion for $Φ^{λ}$ . In the case a,b ∈ K, we prove in addition that a and b must be $̅_{p}$ -linearly dependent.

The Cohen-Lenstra heuristics, moments and $p^{j}$ -ranks of some groups

Christophe Delaunay, Frédéric Jouhet (2014)

Acta Arithmetica

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This article deals with the coherence of the model given by the Cohen-Lenstra heuristic philosophy for class groups and also for their generalizations to Tate-Shafarevich groups. More precisely, our first goal is to extend a previous result due to É. Fouvry and J. Klüners which proves that a conjecture provided by the Cohen-Lenstra philosophy implies another such conjecture. As a consequence of our work, we can deduce, for example, a conjecture for the probability laws of $p^{j}$ -ranks of...

Order of the smallest counterexample to Gallai's conjecture

Fuyuan Chen (2018)

Czechoslovak Mathematical Journal

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In 1966, Gallai conjectured that all the longest paths of a connected graph have a common vertex. Zamfirescu conjectured that the smallest counterexample to Gallai’s conjecture is a graph on 12 vertices. We prove that Gallai’s conjecture is true for every connected graph $G$ with $α^{'} (G) \leq 5$ , which implies that Zamfirescu’s conjecture is true.

On the generalized vanishing conjecture

Zhenzhen Feng, Xiaosong Sun (2019)

Czechoslovak Mathematical Journal

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We show that the GVC (generalized vanishing conjecture) holds for the differential operator $Λ = (\partial_{x} - Φ (\partial_{y})) \partial_{y}$ and all polynomials $P (x, y)$ , where $Φ (t)$ is any polynomial over the base field. The GVC arose from the study of the Jacobian conjecture.

A note on group algebras of $p$ -primary abelian groups

William Ullery (1995)

Commentationes Mathematicae Universitatis Carolinae

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Suppose $p$ is a prime number and $R$ is a commutative ring with unity of characteristic 0 in which $p$ is not a unit. Assume that $G$ and $H$ are $p$ -primary abelian groups such that the respective group algebras $R G$ and $R H$ are $R$ -isomorphic. Under certain restrictions on the ideal structure of $R$ , it is shown that $G$ and $H$ are isomorphic.

A note on Nakai’s conjecture for the ring $K [X ₁, . . ., X ₙ] / (a ₁ X ₁^{m} + \dots + a ₙ X ₙ^{m})$

Paulo Roberto Brumatti, Marcelo Oliveira Veloso (2011)

Colloquium Mathematicae

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On supercharacter theoretic generalizations of monomial groups and Artin's conjecture

Mircea Cimpoeaş, Alexandru Radu (2022)

Czechoslovak Mathematical Journal

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We extend the notions of quasi-monomial groups and almost monomial groups in the framework of supercharacter theories, and we study their connection with Artin’s conjecture regarding the holomorphy of Artin $L$ -functions.