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Длина групповой алгебры прямого произведения циклической группы и циклической p-группы в модулярном случае
Записки научных семинаров ПОМИ РАН. 2023. Т. 524. С. 166–176.
Хрыстик М. А.
конечномерные алгебры, длина алгебры, групповые алгебры, абелевы группы, $p$-группы [finite-dimensional algebras, length of an algebra, group algebras, abelian groups, $p$-groups]
Keywords: abelian groupsабелевы группыгрупповые алгебрыgroup algebrasfinite-dimensional algebras length of an algebra$p$-groupsконечномерные алгебрыдлина алгебры$p$-группы
Publication based on the results of:
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
Added: June 30, 2026
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Ivchenko A., Nigmatullin R. R., Dorokhin S. V., Mathematics 2026 Vol. 9 No. 4 Article 381
n this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider ...
Added: June 27, 2026
Ivchenko A., Шестопёров А. И., Фомина Е. В., Microgravity Science and Technology 2025 Vol. 37 No. 19 P. 1–19
The paper is dedicated to the analysis of medico-biological data obtained during locomotor testing of astronauts. Accurate data interpretation plays a crucial role in locomotion system monitoring, prophylaxis of long-duration spaceflight negative effects and thus in the development of an autonomous medical support system for deep space expeditions. During the locomotor testing the astronaut changes ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., 2023 3rd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET) Mohammedia, Morocco 2023 P. 1–6
The article proposes the architecture for eventdriven Emergency Operation Center with Machine Vision Component. Sources of information are analyzed and approaches to machine vision events for tactical situations detection and estimation are discussed. Messages from Machine Vision Components are converted to Common Alerting Protocol and processed by Operation Center environment for tactical situations recognition. ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., Лукьянченко П. П., Computer Research and Modeling 2023 Vol. 15 No. 1 P. 129–140
In this article we propose a new approach to the analysis of econometric industry parameters for the industry consolidation level. The research is based on the simple industry automatic control model. The state of the industry is measured by quarterly obtained econometric parameters from each industry’s company provided by the tax control regulator. An approach ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., International Frequency Sensor Association (IFSA) Publishing, 19-21 February 2025 Granada, Spain 2025 P. 172–176
The paper presents models for an innovative fully robotic warehouse for storing boxed goods. A discrete multiagent simulation of the movement of shuttles in a warehouse for a given sequence of pallet shipments has been implemented. Different strategies for placement of boxes in various areas of a warehouse are evaluated, as well as optimal routing ...
Added: June 26, 2026
Fedorov Timofey, Moscow Mathematical Journal 2026 Vol. 26 No. 1 P. 73–85
We obtain a complete list of smooth projective threefolds over C for which the dimension of the space of vanishing cycles (in H2(Y,Q) of the smooth hyperplane section Y) equals 2. We also obtain a complete list of rank 2 very ample vector bundles E on smooth projective surfaces with c2(E)=3. ...
Added: June 25, 2026
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций, включенных в программу весенней математической школы. ...
Added: June 25, 2026
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций,
включенных в программу Воронежской зимней матаматической школы С. Г. Крейна - 2026. ...
Added: June 25, 2026
Благовещенская Е. А., Павлова Н. Г., Гарбарук В. В. et al., Международная конференция по мягким вычислениям и измерениям 2018 Т. 1 С. 684–686
Abelian torsion-free groups, being one of the primary algebraic structures, admit an algorithmic approach to the study of their various direct decompositions. The graphs used are of the line-parallel form and they are applicable to parallelization problems. ...
Added: January 13, 2026
Благовещенская Е. А., Гарбарук В. В., Кузнецова И. В. et al., , in: IEEE International Conference on Electrical Engineering and Photonics (EExPolytech).: St. Petersburg: IEEE, 2021. P. 128–131.
Added: January 13, 2026
Благовещенская Е. А., Филимонов А. В., Трифонов А. Е., Journal of Mathematical Sciences 2021 Vol. 259 No. 4 P. 394–402
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Гугнин Д. В., Алгебра и анализ 2025 Т. 37 № 6 С. 90–99
В работе В. М. Бухштабера, А. П. Веселова и А. А. Гайфуллина 2022 года была получена практически полная классификация инволютивных коммутативных двузначных групп. В работе А. А. Гайфуллина 2024 года была доказана автоматическая коммутативность произвольной инволютивной двузначной группы. Единственный вопрос о классификации инволютивных двузначных групп, который оставался открытым после этих публикаций, заключается в следующем: Верно ли, что если две ...
Added: November 13, 2025
Loginov K., Zhang Z., Pinardin A., / Series arXiv "math". 2025.
We study finite abelian groups acting on three-dimensional rationally connected varieties. We concentrate on the groups of K3 type, that is, abelian extensions by a cyclic group of groups that faithfully act on a K3 surface. In particular, if a finite abelian group faithfully acts on a threefold preserving a K3 surface (with at worst ...
Added: September 27, 2025
Хрыстик М. А., Сибирские электронные математические известия 2024 Т. 21 № 2 С. 1132–1144
In this paper, the length of the group algebra of the direct product of a cyclic group and an elementary abelian p-group over a eld of characteristic p is calculated. ...
Added: December 11, 2024
M.A. Khrystik, A.M. Maksaev, Linear Algebra and its Applications 2025 Vol. 704 P. 249–269
Let Mn(F) be the algebra of n×n matrices over a field F and let S be its generating set (as an F-algebra). The length of S is the smallest number k such that Mn(F) equals the F-linear span of all products of the length at most k of matrices from S. The length of Mn(F), denoted by l(Mn(F)), is defined to be the maximal length of any of its generating sets. In 1984, Paz conjectured that l(Mn(F))=2n−2, ...
Added: November 22, 2024
Sergey Mikhailovich Dudakov, Mathematics 2022 Vol. 10 No. 3 Article 533
Let M be a commutative cancellative monoid with an element of infinite order. The binary operation can be extended to all finite subsets of M by the
pointwise definition. So, we can consider the theory of finite subsets of M. Earlier, we have proved the following result: in the theory of finite subsets of M elementary ...
Added: November 12, 2023
Zapryagaev A., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2023 Т. 510 С. 3–7
Büchi arithmetics BAn, , are extensions of Presburger arithmetic with an unary functional symbol
denoting the largest power of n that divides x. Definability of a set in BAn is equivalent to its recognizability
by a finite automaton receiving numbers in their n-ary expansion. We consider the interpretations of Presburger
Arithmetic in the standard model of BAn and ...
Added: July 27, 2023
Semchankau A., Shabanov D. A., Shkredov I., European Journal of Combinatorics 2022 Vol. 100 Article 103453
The paper deals with a problem of Additive Combinatorics. Let G be a finite abelian group of order n. We investigate the number of subset triples (A,B,C) such that for any x from A, y from B, c from C x+y is not equal to z. We prove the tight estimate for this value. As ...
Added: October 26, 2021
Арутюнов А. А., Kosolapov L., Finite Fields and Their Applications 2021 Vol. 76 Article 101921
In this paper we establish decomposition theorems for derivations of group rings. We provide a topological technique for studying derivations of a group ring A[G] in case G has finite conjugacy classes. As a result, we describe all derivations of algebra A[G] for the case when G is a finite group, or G is an FC-group. In addition, we describe an algorithm to explicitly calculate all derivations of ...
Added: October 4, 2021
Buchstaber V., Тертычный С. И., Теоретическая и математическая физика 2020 Т. 204 № 2 С. 153–170
We study properties of the space ΩΩ of solutions of a special double confluent Heun equation closely related to the model of a overdamped Josephson junction. We describe operators acting on ΩΩ and relations in the algebra AA generated by them over the real number field. The structure of AA depends on parameters. We give conditions under which AA is isomorphic to a group algebra ...
Added: June 16, 2021
Mayanskiy E., / Series math "arxiv.org". 2013. No. 5150.
We list all finite abelian groups which act effectively on smooth cubic fourfolds. ...
Added: November 19, 2013