Journal of Pure and Applied Algebra最新文献

英文中文

Finite groups all of whose maximal subgroups have almost odd index 有限群的极大子群都有几乎奇指数

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-10-10 DOI: 10.1016/j.jpaa.2025.108108

Christopher A. Schroeder, Hung P. Tong-Viet

A recurring theme in finite group theory is understanding how the structure of a finite group is determined by the arithmetic properties of group invariants. There are results in the literature determining the structure of finite groups whose irreducible character degrees, conjugacy class sizes or indices of maximal subgroups are odd. These results have been extended to include those finite groups whose character degrees or conjugacy class sizes are not divisible by 4. In this paper, we determine the structure of finite groups whose maximal subgroups have index not divisible by 4. As an application, we obtain some new 2-nilpotency criteria.

在有限群论中反复出现的主题是理解有限群的结构是如何由群不变量的算术性质决定的。文献中有关于不可约特征度、共轭类大小或极大子群指标为奇数的有限群结构的确定结果。这些结果被推广到包括那些特征度或共轭类大小不能被4整除的有限群。本文确定了极大子群的索引不能被4整除的有限群的结构。作为应用，我们得到了一些新的2-幂零判据。

引用次数: 0

Computing epsilon multiplicities in graded algebras 在分级代数中计算epsilon多重性

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-10-06 DOI: 10.1016/j.jpaa.2025.108107

Suprajo Das , Saipriya Dubey , Sudeshna Roy , Jugal K. Verma

This article investigates the computational aspects of the ε-multiplicity. Primarily, we show that the ε-multiplicity of a homogeneous ideal I in a two-dimensional standard graded domain of finite type over an algebraically closed field of arbitrary characteristic, is always a rational number. In this situation, we produce a formula for the ε-multiplicity of I in terms of certain mixed multiplicities associated to I. In any dimension, under the assumptions that the saturated Rees algebra of I is finitely generated, we give a different expression of the ε-multiplicity in terms of mixed multiplicities by using the Veronese degree. This enabled us to make various explicit computations of ε-multiplicities. We further write a Macaulay2 algorithm to compute ε-multiplicity (under the Noetherian hypotheses) even when the base ring is not necessarily standard graded.

本文研究了ε-多重性的计算问题。首先，我们证明了任意特征的代数闭域上二维有限型标准梯度域上齐次理想I的ε-复数总是有理数。在这种情况下，我们用与I相关的某些混合复数来表示I的ε-复数。在任何维度上，假设I的饱和Rees代数是有限生成的，我们用维罗内塞度给出了混合复数表示的ε-复数的不同表达式。这使我们能够对ε-复数进行各种显式计算。我们进一步编写了Macaulay2算法来计算ε-多重性（在Noetherian假设下），即使基环不一定是标准分级的。

引用次数: 0

Functorial, operadic and modular operadic combinatorics of circuit algebras 电路代数的泛函、操作及模操作组合

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-10-01 DOI: 10.1016/j.jpaa.2025.108105

Sophie Raynor

Circuit algebras are a symmetric analogue of Jones's planar algebras introduced to study finite-type invariants of virtual knotted objects. Circuit algebra structures appear, in different forms, across mathematics. This paper provides a dictionary for translating between their diverse incarnations and describing their wider context. A formal definition of a broad class of circuit algebras is established and three equivalent descriptions of circuit algebras are provided: in terms of operads of wiring diagrams, modular operads and categories of Brauer diagrams. As an application, circuit algebra characterisations of algebras over the orthogonal and symplectic groups are given.

电路代数是琼斯平面代数的对称模拟，用于研究虚结对象的有限型不变量。电路代数结构以不同的形式出现在数学中。本文提供了一个词典，用于翻译他们不同的化身和描述他们更广泛的背景。建立了一大类电路代数的形式化定义，并给出了电路代数的三种等价描述：根据接线图的操作数、模操作数和布劳尔图的范畴。作为应用，给出了正交群和辛群上代数的电路代数特征。

引用次数: 0

Hypergeometric sheaves and extraspecial groups in even characteristic 偶特征中的超几何轴和超特殊群

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-10-01 DOI: 10.1016/j.jpaa.2025.108106

Lee Tae Young

We determine precisely which irreducible hypergeometric sheaves have an extraspecial normalizer in characteristic 2 as their geometric monodromy groups. This resolves the last open case of the classification of local monodromy at 0 of irreducible hypergeometric sheaves with finite geometric monodromy group.

我们精确地确定了哪些不可约超几何轴在其几何单群中具有特征2上的特外规格化子。这解决了具有有限几何单群的不可约超几何轴在0处局部单分类的最后一个开放情况。

引用次数: 0

Rational quartic curves in the Mukai-Umemura variety Mukai-Umemura品种的有理四次曲线

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-10-01 DOI: 10.1016/j.jpaa.2025.108102

Kiryong Chung , Jaehyun Kim , Jeong-Seop Kim

Let X be a Fano threefold of index one and degree 22 with

Pic (X) ≅ Z

. Such a threefold X can be realized as the zero locus of a regular section s of

{(⋀^{2} U^{⁎})}^{\oplus 3}

over the Grassmannian

Gr (3, V)

, where

\dim V = 7

and

U

is the universal subbundle. When the section s is given by the net of the

{SL}_{2}

-invariant skew-symmetric forms, we call it the Mukai-Umemura (MU) variety. In this paper, we prove that the Hilbert scheme of rational quartic curves in the MU-variety is smooth, and we compute its Poincaré polynomial by applying Białynicki-Birula's theorem.

设X是一个指标为1，次为22的Fano三次函数，且具有Pic(X) = Z。这样的三重X可以被实现为格拉斯曼Gr（3，V）上的正则截面s的零轨迹，其中dim (V) =7， U是泛子束。当截面s由sl2不变偏对称形式的网给出时，我们称其为Mukai-Umemura （MU）变体。本文证明了mu -变量中有理四次曲线的Hilbert格式是光滑的，并应用Białynicki-Birula定理计算了它的poincar多项式。

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引用次数: 0

The F-pure threshold of a Schubert cycle 舒伯特循环的f -纯阈值

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-10-01 DOI: 10.1016/j.jpaa.2025.108104

Justin Fong , Mitsuhiro Miyazaki

The F-pure threshold is the characteristic p counter part of the log canonical threshold in characteristic zero. It is a numerical invariant associated to the singularities of a variety, hence computing its value is important. We give a closed formula for the F-pure threshold of the irrelevant maximal ideal of Schubert cycles, which are the homogeneous coordinate rings of Schubert subvarieties of a Grassmannian. The main point of the computation is to give an explicit formula for the a-invariant of a Schubert cycle. The derivation of both formulas is made possible through the combinatorics of the underlying poset of these rings.

f -纯阈值是特征0中对数正则阈值的特征p计数器部分。它是一个与各种奇点有关的数值不变量，因此计算它的值是很重要的。我们给出了无关极大理想Schubert环的f -纯阈值的一个封闭公式，Schubert环是一类Grassmannian的Schubert子变量的齐次坐标环。计算的重点是给出舒伯特循环的a不变量的显式公式。这两个公式的推导是通过对这些环的基本偏序集的组合而实现的。

引用次数: 0

Noether's normalization in skew polynomial rings 歪斜多项式环中的Noether归一化

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-10-01 DOI: 10.1016/j.jpaa.2025.108101

Elad Paran , Thieu N. Vo

We study Noether's normalization lemma for finitely generated algebras over a division algebra. In its classical form, the lemma states that if I is a proper ideal of the ring

R = F [t_{1}, \dots, t_{n}]

of polynomials over a field F, then the quotient ring

R / I

is a finite extension of a polynomial ring over F. We prove that the lemma holds when

R = D [t_{1}, \dots, t_{n}]

is the ring of polynomials in n central variables over a division algebra D. We provide examples demonstrating that Noether's normalization may fail for the skew polynomial ring

D [t_{1}, \dots, t_{n}; σ_{1}, \dots, σ_{n}]

with respect to commuting automorphisms

σ_{1}, \dots, σ_{n}

of D. We give a sufficient condition for

σ_{1}, \dots, σ_{n}

under which the normalization lemma holds for such ring. In the case where

D = F

is a field, this sufficient condition is proved to be necessary.

研究了除法代数上有限生成代数的Noether归一化引理。经典形式的引理表明，如果I是域F上多项式环R=F[t1，…，tn]的固有理想，则商环R/I是F上多项式环的有限扩展。我们证明了当R=D[t1，…，tn]是除法代数D上n个中心变量的多项式环时，引理成立。我们提供了例子证明了对于偏多项式环D[t1，…，tn] Noether的归一化可能失败；d的交换自同构σ1，…，σn]，给出了σ1，…，σn的一个充分条件，在这个条件下，这种环的归一化引理成立。在D=F为域的情况下，证明了这个充分条件是必要的。

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引用次数: 0

On the standard models of del Pezzo fibrations of degree four 关于四阶del Pezzo振动的标准模型

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-10-01 DOI: 10.1016/j.jpaa.2025.108103

Natsume Kitagawa

Corti defined the notion of standard models of del Pezzo fibrations, and studied their existence over

C

with a fixed generic fibre in [6]. In this paper, we prove the existence of standard models of del Pezzo fibrations of degree 4 in characteristic >2. To show this, we use the notion of Kollár stability, which was introduced in [12] and [1].

Corti定义了del Pezzo纤维的标准模型的概念，并在b[6]中研究了它们在C上的存在性。本文证明了特征度为4的del Pezzo振动标准模型的存在性。为了说明这一点，我们使用了在[12]和[1]中引入的Kollár稳定性的概念。

引用次数: 0

Orbits on a product of two flags and a line and the Bruhat order, I 轨道是由两面旗帜和一条线以及布鲁哈特命令组成的

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-09-29 DOI: 10.1016/j.jpaa.2025.108100

Mark Colarusso , Sam Evens

<div><div>Let <math><mi>G</mi><mo>=</mo><mi>G</mi><mi>L</mi><mo>(</mo><mi>n</mi><mo>)</mo></math> be the <math><mi>n</mi><mo>×</mo><mi>n</mi></math> complex general linear group and let <math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math> be its flag variety. The standard Borel subgroup B of upper triangular matrices acts on the product <math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>×</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math> diagonally with finitely many orbits. In this paper, we study the B-orbits on the subvarieties <math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>×</mo><msub><mrow><mi>O</mi></mrow><mrow><mi>i</mi></mrow></msub></math>, where <math><msub><mrow><mi>O</mi></mrow><mrow><mi>i</mi></mrow></msub></math> is the B-orbit on <math><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math> containing the line through the origin in the direction of the i-th standard basis vector of <math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math>. For each <math><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi></math>, we construct a bijection between B-orbits on <math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>×</mo><msub><mrow><mi>O</mi></mrow><mrow><mi>i</mi></mrow></msub></math> and certain pairs of Schubert cells in <math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>×</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math>. We also show that this bijection can be used to understand the Richardson-Springer monoid action on such B-orbits in terms of the classical monoid action of the symmetric group on itself. We also develop combinatorial models of these orbits and use these models to compute exponential generating functions for the sequences <math><msub><mrow><mo>{</mo><mo>|</mo><mi>B</mi><mo>﹨</mo><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>×</mo><msub><mrow><mi>O</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>|</mo><mo>}</mo></mrow><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></msub></math> and <math><msub><mrow><mo>{</mo><mo>|</mo><mi>B</mi><mo>﹨</mo><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>×</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo><mo>|</mo><mo>}</mo></mrow><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></msub></math>. In the sequel to this paper, we use the results of this paper to construct a correspondence between B-orbits on <math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>×</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn>

设G=GL(n)为n×n复一般线性群，设Bn为其标志簇。上三角矩阵的标准Borel子群B作用于乘积Bn×Pn−1与有限多轨道对角线。本文研究了子集Bn×Oi上的b轨道，其中Oi是Pn−1上的b轨道，其中包含了沿Cn的第i个标准基向量方向穿过原点的直线。对于每个i=1，…，n，我们在Bn×Oi上的b轨道和Bn×Bn上的某些Schubert细胞对之间构造一个双射。我们还证明了这种双射可以用对称群对自身的经典单群作用来理解b轨道上的Richardson-Springer单群作用。我们还建立了这些轨道的组合模型，并使用这些模型计算了序列{|B(Bn×Oi)|}n≥1和{|B(Bn×Pn−1)|}n≥1的指数生成函数。在本文的续文中，我们利用本文的结果构造了Bn×Pn−1上的b轨道与GL（n+1）的标志簇Bn+1上的b轨道集合之间的对应关系，并证明了这种对应关系尊重闭包关系并保留了单群作用。因此，利用我们在[1]中的结果，可以通过Bruhat阶来理解Bn×Pn−1上所有b轨道集合上的闭包关系和幺正作用。

引用次数: 0

On the spectrum of residual finiteness growth functions 残差有限生长函数的谱

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-09-25 DOI: 10.1016/j.jpaa.2025.108099

Henry Bradford

In [4] Bou-Rabee and Seward constructed examples of finitely generated residually finite groups G whose residual finiteness growth function

F_{G}

can be at least as fast as any prescribed function. In this note we describe a modified version of their construction, which allows us to give a complementary upper bound on

F_{G}

. As such, every nondecreasing function at least

\exp (n \log {(n)}^{2} \log \log {(n)}^{1 + ϵ})

is close to the residual finiteness growth function of some finitely generated group. We also have similar result for the full residual finiteness growth function and for the divisibility function.

在1996年，boub - rabee和Seward构造了有限生成的剩余有限群G的例子，其剩余有限生长函数FG至少可以与任何规定函数一样快。在本文中，我们描述了它们构造的一个改进版本，它允许我们给出FG上的一个互补上界。因此，每一个至少为exp (nlog （n)2log (log)1+ λ）的非递减函数都接近于某个有限生成群的残差有限生长函数。对于完全剩余有限生长函数和可整除函数，我们也有类似的结果。

引用次数: 0

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Journal of Pure and Applied Algebra

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