Results 21 to 30 of about 23,662 (137)

The first two group theory papers of Philip Hall

Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.
Abstract In this paper, we discuss the first two papers on soluble groups written by Philip Hall and their influence on the study of finite groups. The papers appeared in 1928 and 1937 in the Journal of the London Mathematical Society.
Inna Capdeboscq
wiley   +1 more source

Semi-galois Categories II: An arithmetic analogue of Christol's theorem

, 2018
In connection with our previous work on semi-galois categories, this paper proves an arithmetic analogue of Christol's theorem concerning an automata-theoretic characterization of when a formal power series over finite field is algebraic over the ...
Uramoto, Takeo
core   +1 more source

The modular automorphisms of quotient modular curves

Mathematika, Volume 72, Issue 1, January 2026.
Abstract We obtain the modular automorphism group of any quotient modular curve of level N$N$, with 4,9∤N$4,9\nmid N$. In particular, we obtain some unexpected automorphisms of order 3 that appear for the quotient modular curves when the Atkin–Lehner involution w25$w_{25}$ belongs to the quotient modular group. We also prove that such automorphisms are
Francesc Bars, Tarun Dalal
wiley   +1 more source

Real difference Galois theory

, 2017
In this paper, we develop a difference Galois theory in the setting of real fields. After proving the existence and uniqueness of the real Picard-Vessiot extension, we define the real difference Galois group and prove a Galois correspondence.Comment ...
Dreyfus, Thomas
core   +2 more sources

Nontriviality of rings of integral‐valued polynomials

Mathematische Nachrichten, Volume 298, Issue 12, Page 3974-3994, December 2025.
Abstract Let S$S$ be a subset of Z¯$\overline{\mathbb {Z}}$, the ring of all algebraic integers. A polynomial f∈Q[X]$f \in \mathbb {Q}[X]$ is said to be integral‐valued on S$S$ if f(s)∈Z¯$f(s) \in \overline{\mathbb {Z}}$ for all s∈S$s \in S$. The set IntQ(S,Z¯)${\mathrm{Int}}_{\mathbb{Q}}(S,\bar{\mathbb{Z}})$ of all integral‐valued polynomials on S$S ...
Giulio Peruginelli, Nicholas J. Werner
wiley   +1 more source

On separable algebras in Grothendieck Galois theory

Le Matematiche, 1996
We give an explicit proof of the fundamental theorem of Grothendieck Galois theory: the category of separable algebras over a field K is anti-equivalent to the category of continuous actions on finite sets of the profinite fundamental group of K.
Federico G. Lastaria
doaj  

Vladimirov–Pearson operators on ζ$\zeta$‐regular ultrametric Cantor sets

Mathematische Nachrichten, Volume 298, Issue 12, Page 3779-3790, December 2025.
Abstract A new operator for certain types of ultrametric Cantor sets is constructed using the measure coming from the spectral triple associated with the Cantor set, as well as its zeta function. Under certain mild conditions on that measure, it is shown that it is an integral operator similar to the Vladimirov–Taibleson operator on the p$p$‐adic ...
Patrick Erik Bradley
wiley   +1 more source

Applications of Galois Theory

Journal of Nepal Mathematical Society
This paper gives an insight to the Galois theory and discusses its applications in both pure and applied mathematics. First, the Fundamental theorem of Galois theory is applied to compute the Galois groups of polynomials and to prove the non-existence of
Sandesh Thakuri, Bishnu H Subedi
semanticscholar   +1 more source

Chebotarev's theorem for cyclic groups of order pq$pq$ and an uncertainty principle

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3841-3856, December 2025.
Abstract Let p$p$ be a prime number and ζp$\zeta _p$ a primitive p$p$th root of unity. Chebotarev's theorem states that every square submatrix of the p×p$p \times p$ matrix (ζpij)i,j=0p−1$(\zeta _p^{ij})_{i,j=0}^{p-1}$ is nonsingular. In this paper, we prove the same for principal submatrices of (ζnij)i,j=0n−1$(\zeta _n^{ij})_{i,j=0}^{n-1}$, when n=pr ...
Maria Loukaki
wiley   +1 more source

Category Theory and Galois Theory [PDF]

, 2017
Galois theory translates questions about fields into questions about groups. The fundamental theorem of Galois theory states that there is a bijection between the intermediate fields of a field extension and the subgroups of the corresponding Galois ...
Bower, Amanda
core   +1 more source