УДК 512.542
MSC: 20B25, 05C12, 05C25, 05C50, 05E30, 20D05, 20D06, 20D08, 20D10, 20D20, 20D25, 20D40, 20D60, 20D99, 20E32, 20E34, 20E45, 20F16, 20F50
DOI: 10.21538/0134-4889-2024-30-1-284-293
PDF (Open Access)
A review of the main events of the 2023 Ural Workshop on Group Theory and Combinatorics, held online during the period 21 to 27 August 2023, is presented, and a list of open problems with comments is given. Open problems were formulated by the participants at the Open Problems Session held on August 27, 2023.
Keywords: power graph, enhanced power graph, independence graph of a group, rank graph of a group, finite group, isomorphism of groups, π-solvable group, simple group, average element order, solvable group, deficient element, locally finite group, distance-regular graph, Krein graph, strongly regular graph, Gruenberg–Kegel graph (prime graph), almost simple group, Cayley graph, clique graph, edge-transitive graph, normal cover of a graph, 2-arc-transitive graph, semisymmetric graph, complete class of groups, Baer–Suzuki width, symmetric boundary of a class of groups
REFERENCES
1. 2023 Ural Workshop on Group Theory and Combinatorics [e-resource] . Available on: http://2023uwgtc.imm.uran.ru
2. N.N. Krasovskii Institute of Mathematics and Mechanics [e-resource] . Available on: https://www.imm.uran.ru/eng
3. Institute of Natural Sciences and Mathematics, Ural Federal University, Russia [e-resource] (in Russian). Available on: https://insma.urfu.ru/ru/
4. Ural Mathematical Center [e-resource] . Available on: https://umc.urfu.ru/en/
5. Ural Seminar on Group Theory and Combinatorics [e-resource] . Available on: https://http://uwgtc.imm.uran.ru
6. Cameron P.J., Maslova N.V. Criterion of unrecognizability of a finite group by its Gruenberg–Kegel graph. J. Algebra, 2022, vol. 607, part A, pp. 186–213. doi: 10.1016/j.jalgebra.2021.12.005
7. Freedman S.D., Lucchini A., Nemmi D., Roney-Dougal C.M. Finite groups satisfying the independence property. International Journal of Algebra and Computation, 2023, vol. 33, no. 3, pp. 509–545. doi: 10.1142/S021819672350025X
8. Biswas S., Cameron P.J., Das A., Dey H.K. On difference of enhanced power graph and power graph of a finite group. Available on: arXiv:2206.12422 [math.CO]. doi: 10.48550/arXiv.2206.12422
9. The Kourovka notebook. Unsolved problems in group theory, 20th ed., eds. V.D. Mazurov, E.I. Khukhro. Novosibirsk, Inst. Math. SO RAN Publ., 2022, 269 p. Available at: https://kourovka-notebook.org/.
10. Khukhro E.I., Moretó A., Zarrin M. The average element order and the number of conjugacy classes of finite groups. J. Algebra, 2021, vol. 569, no. 1, pp. 1–11. doi: 10.1016/j.jalgebra.2020.11.009
11. Herzog M., Longobardi P., Maj M. Another criterion for solvability of finite groups. J. Algebra, 2022, vol. 597, pp. 1–23. doi: 10.1016/j.jalgebra.2022.01.005
12. Herzog M., Longobardi P., Maj M. On groups with average element orders equal to the average order of the alternating group of degree 5. Glasnik Matematicki, 2023, vol. 58, no. 2, pp. 307–315. doi: 10.3336/gm.58.2.10
13. Herzog M., Longobardi P., Maj M. On $\mathcal{D}(j)$-groups with an element of order $p^{j+1}$, in preparation.
14. Maslova N.V., Panshin V.V., Staroletov A.M. On characterization by Gruenberg–Kegel graph of finite simple exceptional groups of Lie type. European J. Math., 2023, vol. 9, art. no. 78. doi: 10.1007/s40879-023-00672-7
15. Hawtin D.R., Praeger C.E., Zhou JX. Using mixed dihedral groups to construct normal Cayley graphs and a new bipartite 2-arc-transitive graph which is not a Cayley graph. J. Algebr. Comb., 2024, 14 p. doi: 10.1007/s10801-024-01300-7
16. Gordeev N., Grunewald F., Kunyavskii B., Plotkin E. A description of Baer–Suzuki type of the solvable radical of a finite group. J. Pure Appl. Algebra, 2009, vol. 213, no. 2, pp. 250–258. doi: 10.1016/j.jpaa.2008.06.006
17. H. Wielandt. Zusammengesetzte Gruppen endlicher Ordnung. In: Lecture Notes, Math. Inst. Univ. TЈubingen, 1963/64, Mathematische Werke / Mathematical Works, vol. 1, Group Theory, Berlin: Walter de Gruyter and Co., 1994, pp. 607–655.
Received February 18, 2024
Revised February 25, 2024
Accepted February 28, 2024
Funding Agency: The author of this survey paper gratefully acknowledges the research funding from the Ministry of Science and Higher Education of the Russian Federation (project 075-02-2024-1428 for the development of the Regional Scientific and Educational Mathematical Center “Ural Mathematical Center”).
Natalia Vladimirovna Maslova, Dr. Phys.-Math. Sci., Leading Research Fellow, N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Professor, Ural Federal University, Yekaterinburg, 620083 Russia; Leading Research Fellow, Ural Mathematical Center, Yekaterinburg, 620083 Russia, e-mail: butterson@mail.ru.
Cite this article as: N.V. Maslova. 2023 Ural Workshop on Group Theory and Combinatorics, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, vol. 30, no. 1, pp. 284–293.
Русский
Н.В. Маслова. Международная конференция “2023 Ural Workshop on Group Theory and Combinatorics”
В статье представлен обзор основных событий Международной конференции “2023 Ural Workshop on Group Theory and Combinatorics”, которая прошла в онлайн формате 21–27 августа 2023 г. Также в статье представлен список открытых проблем, сформулированных участниками на Часе открытых проблем, прошедшем 27 августа 2023 г., и комментарии к этим проблемам.
Ключевые слова: граф степеней, расширенный граф степеней, граф независимости группы, ранговый граф группы, конечная группа, изоморфизм групп, π-разрешимая группа, простая группа, средний порядок элемента, разрешимая группа, дефицитный элемент, локально конечная группа, дистанционно регулярный граф, граф Крейна, сильно регулярный граф, граф Грюнберга–Кегеля (граф простых чисел), почти простая группа, граф Кэли, кликовый граф, реберно-транстранзитивный граф, нормальное накрытие графа, дважды транзитивный на дугах граф, полусимметричный граф, полный класс групп, ширина Бэра–Судзуки, симметрическая граница класса групп
