International Journal of Algebra and Computation最新文献

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A branch group in a class of non-contracting weakly regular branch groups 一类非收缩弱正则分支群中的分支群

IF 0.5 2区数学 Q3 MATHEMATICS

International Journal of Algebra and Computation

Pub Date : 2024-07-05 DOI: 10.1142/s021819672450036x

Sagar Saha, K. V. Krishna

引用次数: 0

On the dimensions of the graded space 𝔽2 ⊗𝒜𝔽2[x1,x2,…,xs] at degrees s + 5 and its relation to algebraic transfers 论 s + 5 度的梯度空间𝔽2 ⊗𝒜𝔽2[x1,x2,...,xs] 的维数及其与代数转移的关系

IF 0.5 2区数学 Q3 MATHEMATICS

International Journal of Algebra and Computation

Pub Date : 2024-07-05 DOI: 10.1142/s0218196724500401

Dang Vo Phuc

引用次数: 0

On the representation of fields as sums of two proper subfields 论场作为两个适当子场之和的表示法

IF 0.5 2区数学 Q3 MATHEMATICS

International Journal of Algebra and Computation

Pub Date : 2024-07-05 DOI: 10.1142/s0218196724500395

M. Kepczyk

引用次数: 0

Clonoids between modules 模块之间的克隆体

IF 0.8 2区数学 Q3 Mathematics

International Journal of Algebra and Computation

Pub Date : 2024-05-25 DOI: 10.1142/s021819672450022x

Peter Mayr, Patrick Wynne

Clonoids are sets of finitary functions from an algebra $A$ to an algebra $B$ that are closed under composition with term functions of $A$ on the domain side and with term functions of $B$ on the codomain side. For $A, B$ (polynomially equivalent to) finite modules we show: If $A, B$ have coprime order and the congruence lattice of $A$ is distributive, then there are only finitely many clonoids from $A$ to $B$ . This is proved by establishing for every natural number $k$ a particular linear equation that all $k$ -ary functions from $A$ to $B$ satisfy. Else if $A, B$ do not have coprime order, then there exist infinite ascending chains of clonoids from $A$ to $B$ ordered by inclusion. Consequently any extension of $A$ by $B$ has countably infinitely many <

有限模块是指从代数 A 到代数 B 的有限函数集合，这些函数在与域边上的 A 的项函数和同域边上的 B 的项函数的组合下是封闭的。对于 A、B（多项式等价于）有限模块，我们证明：如果 A、B 有共阶，且 A 的全等网格是分布式的，那么从 A 到 B 只有有限多个克隆子。这可以通过为每个自然数 k 建立一个特定的线性方程来证明，从 A 到 B 的所有 kary 函数都满足这个方程。否则，如果 A、B 没有共序，那么就存在从 A 到 B 按包含排序的无限递增的克隆子链。因此，任何由 B 扩展的 A 都有可数的无限多个 2-nilpotent 扩展，直到项等价。

引用次数: 0

There are no post-quantum weakly pseudo-free families in any nontrivial variety of expanded groups 在任何非数量级的扩展群中都不存在后量子弱伪自由族

IF 0.8 2区数学 Q3 Mathematics

International Journal of Algebra and Computation

Pub Date : 2024-05-17 DOI: 10.1142/s0218196724500188

Mikhail Anokhin

Let $Ω$ be a finite set of finitary operation symbols and let $𝔙$ be a nontrivial variety of $Ω$ -algebras. Assume that for some set $Γ \subseteq Ω$ of group operation symbols, all $Ω$ -algebras in $𝔙$ are groups under the operations associated with the symbols in $Γ$ . In other words, $𝔙$ is assumed to be a nontrivial variety of expanded groups. In particular, $𝔙$ can be a nontrivial variety of groups or rings. Our main result is that there are no post-quantum weakly pseudo-free families in $𝔙$ , even in the worst-case setting and/or the black-box model. In this paper, we restrict ourselves to families $(H_{d} |d \in D)$ of computational and black-box $Ω$ -algebras (where $D \subseteq {0, 1}^{*}$ ) such that for every $d \in D$ , each element of $H_{d}$ is represented by a unique bit string of length polynomial in the length of $d$ . In our main result, we use straight-line programs to represent nontrivial relations between elements of $Ω$ -algebras. Note that under certain conditions, this result depends on the classification of finite simple gr

让 Ω 是有限运算符号集，让 𝔙 是 Ω-gebras 的非奇异集合。假设对于某个群运算符号集 Γ⊆Ω，𝔙 中的所有 Ω-gebras 在与Γ 中符号相关的运算下都是群。换句话说，我们假定𝔙 是一个扩展群的非小类。特别是，𝔙 可以是群或环的一个非私密种类。我们的主要结果是，即使在最坏情况设置和/或黑箱模型中，𝔙中也不存在后量子弱无伪族。在本文中，我们将自己限制在计算和黑箱Ω-数组（其中 D⊆{0,1}∗）的族 (Hd|d∈D)，这样对于每个 d∈D，Hd 的每个元素都由长度与 d 的长度成多项式的唯一比特串来表示。请注意，在某些条件下，这一结果取决于有限简单群的分类。此外，我们还定义并研究了计算和黑盒子Ω玻家族的一些后量子弱伪无穷性类型。

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引用次数: 0

On the lattice of closed subgroups of a profinite group 论无限群的封闭子群网格

IF 0.8 2区数学 Q3 Mathematics

International Journal of Algebra and Computation

Pub Date : 2024-05-09 DOI: 10.1142/s0218196724500206

Francesco de Giovanni, Iker de las Heras, Marco Trombetti

The subgroup lattice of a group is a great source of information about the structure of the group itself. The aim of this paper is to use a similar tool for studying profinite groups. In more detail, we study the lattices of closed or open subgroups of a profinite group and its relation with the whole group. We show, for example, that procyclic groups are the only profinite groups with a distributive lattice of closed or open subgroups, and we give a sharp characterization of profinite groups whose lattice of closed (or open) subgroups satisfies the Dedekind modular law; we actually give a precise description of the behavior of modular elements of the lattice of closed subgroups. We also deal with the problem of carrying some structural information from a profinite group to another one having an isomorphic lattice of closed (or open) subgroups. Some interesting consequences and related results concerning decomposability and the number of profinite groups with a given lattice of closed (or open) subgroups are also obtained.

一个群的子群网格是有关群本身结构的重要信息来源。本文旨在使用类似的工具来研究无限群。我们将更详细地研究无限群的封闭子群或开放子群的网格及其与整个群的关系。例如，我们证明了原环群是唯一具有封闭子群或开放子群的分布晶格的无限群，并给出了封闭（或开放）子群晶格满足戴德金模态律的无限群的尖锐特征；实际上，我们给出了封闭子群晶格的模态元素行为的精确描述。我们还处理了从一个无限群到另一个具有同构封闭（或开放）子群网格的无限群之间传递某些结构信息的问题。此外，我们还得到了一些有趣的结果以及与可分解性和具有给定封闭（或开放）子群网格的无限群数量有关的相关结果。

引用次数: 0

An algorithm to recognize echelon subgroups of a free group 识别自由群梯形子群的算法

IF 0.8 2区数学 Q3 Mathematics

International Journal of Algebra and Computation

Pub Date : 2024-04-30 DOI: 10.1142/s021819672450019x

Dario Ascari

We provide an algorithm that, given a finite set of generators for a subgroup $H$ of a finitely generated free group $F$ , determines whether $H$ is echelon or not and, in case of affirmative answer, also computes a basis with respect to which $H$ is in echelon form. This gives an answer to a question of Rosenmann. We also prove, by means of a counterexample, that intersection of two echelon subgroups needs not to be echelon, answering another question of Rosenmann.

我们提供了一种算法，只要给定有限生成的自由群 F 的子群 H 的有限生成子集，就能确定 H 是否为梯形，如果答案是肯定的，还能计算出 H 为梯形的基。这就回答了罗森曼的一个问题。我们还通过一个反例证明了两个梯形子群的交集不一定是梯形，从而回答了罗森曼的另一个问题。

引用次数: 0

Properties of congruence lattices of graph inverse semigroups 图逆半群全等网格的性质

IF 0.8 2区数学 Q3 Mathematics

International Journal of Algebra and Computation

Pub Date : 2024-04-20 DOI: 10.1142/s0218196724500139

Marina Anagnostopoulou-Merkouri, Zachary Mesyan, James D. Mitchell

From any directed graph $E$ one can construct the graph inverse semigroup $G (E)$ , whose elements, roughly speaking, correspond to paths in $E$ . Wang and Luo showed that the congruence lattice $L (G (E))$ of $G (E)$ is upper-semimodular for every graph $E$ , but can fail to be lower-semimodular for some $E$ . We provide a simple characterization of the graphs $E$ for which $L (G (E))$ is lower-semimodular. We also describe those $E$ such that $L (G (E))$ is atomistic, and characterize the minimal generating sets for $L (G (E))$ when $E$ is finite and simple.

王和罗（Wang and Luo）的研究表明，G(E) 的同余网格 L(G(E)) 对于每个图 E 都是上半模的，但对于某些图 E 可能不是下半模的。我们还描述了那些 L(G(E)) 原子化的 E，并描述了当 E 有限且简单时 L(G(E)) 的最小生成集。

引用次数: 0

Dependence over subgroups of free groups 对自由群子群的依赖性

IF 0.8 2区数学 Q3 Mathematics

International Journal of Algebra and Computation

Pub Date : 2024-04-05 DOI: 10.1142/s0218196724500176

A. Rosenmann, Enric Ventura

引用次数: 0

p-Singular characters and normal sylow p-subgroups p 星形字符和正常低 p 子群

IF 0.8 2区数学 Q3 Mathematics

International Journal of Algebra and Computation

Pub Date : 2024-04-05 DOI: 10.1142/s0218196724500164

Weijun Liu, Qinghong Guo, Lihua Feng, Zheng Huang

引用次数: 0

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