Generalizations of the Fitting subgroup and the hypercenter of a finite group.
Main publications:
V. I. Murashka, “Classes of finite groups with generalized subnormal cyclic primary subgroups”, Sibirsk. Mat. Zh., 55:6 (2014), 1353–1367; Siberian Math. J., 55:6 (2014), 1105–1115
V. I. Murashka, “On Shemetkov's Question about the $\mathfrak{F}$-Hypercenter”, Mat. Zametki, 115:5 (2024), 759–771; Math. Notes, 115:5 (2024), 779–788
S. V. Balychev, A. F. Vasil'ev, V. I. Murashka, “On the formations of finite solvable groups with property ${\mathcal P}_{2}$”, Sibirsk. Mat. Zh., 65:6 (2024), 1102–1114; Siberian Math. J., 65:6 (2024), 1281–1291
3.
V. I. Murashka, “On the classes of finite groups defined by the systems of generalized subnormal subgroups”, Proceedings of the Institute of Mathematics of the NAS of Belarus, 32:1 (2024), 25–30
4.
S. V. Balychev, V. I. Murashka, “On the influence of the $\mathfrak{F}$-hypercenter on the structure of finite multifactorized groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 30:4 (2024), 55–63
2023
5.
V. I. Murashko, A. F. Vasil'ev, “A functorial generalization of the Fitting subgroup in finite groups”, Algebra Logika, 62:5 (2023), 593–613
6.
V. I. Murashka, “Arithmetic graphs and factorized finite groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 29:4 (2023), 181–192
2022
7.
V. I. Murashka, “On Questions Posed by Shemetkov, Ballester-Bolinches, and Perez-Ramos in Finite Group Theory”, Mat. Zametki, 112:6 (2022), 839–849; Math. Notes, 112:6 (2022), 932–939
A. F. Vasil'ev, V. I. Murashka, A. K. Furs, “Finite Groups with Three Nonconjugate Maximal Formational Subgroups”, Mat. Zametki, 111:3 (2022), 354–364; Math. Notes, 111:3 (2022), 356–363
A. F. Vasil'ev, V. I. Murashka, A. K. Furs, “On the Hawkes graphs of finite groups”, Sibirsk. Mat. Zh., 63:5 (2022), 1010–1026; Siberian Math. J., 63:5 (2022), 849–861
A. F. Vasil'ev, V. I. Murashka, “Formations and Products of $\mathrm F(G)$-Subnormal Subgroups of Finite Solvable Groups”, Mat. Zametki, 107:3 (2020), 376–390; Math. Notes, 107:3 (2020), 413–424
V. I. Murashka, A. A. Piachonkin, “On the number of points on one class of curves in a ring of residues”, PFMT, 2020, no. 4(45), 98–104
13.
S. M. Gorsky, V. I. Murashka, “$\mathfrak{H}_p\mathfrak{H}_q$-convex functions and generalization of the Hölder, Minkowski, and Muirhead inequalities”, PFMT, 2020, no. 3(44), 61–66
2019
14.
V. I. Murashka, “On the $\mathfrak{F}$-hypercentral subgroups with the sylow tower property of finite groups”, Chebyshevskii Sb., 20:2 (2019), 391–398
15.
V. I. Murashka, “Generalized rank composition formations of finite groups”, PFMT, 2019, no. 3(40), 93–99
16.
V. I. Murashka, “Groups with prescribed systems of Schmidt subgroups”, Sibirsk. Mat. Zh., 60:2 (2019), 429–440; Siberian Math. J., 60:2 (2019), 334–342
A. F. Vasilyev, V. I. Murashka, “Arithmetic graphs and classes of finite groups”, Sibirsk. Mat. Zh., 60:1 (2019), 55–73; Siberian Math. J., 60:1 (2019), 41–55
V. I. Murashka, S. M. Gorsky, Ya. I. Sandryhaila, “$\mathfrak{K}_{\varphi}\mathfrak{K}_{\psi}$-convex functions and generalizations of classical inequalities”, PFMT, 2018, no. 4(37), 98–102
V. I. Murashka, “Classes of finite groups with generalized subnormal cyclic primary subgroups”, Sibirsk. Mat. Zh., 55:6 (2014), 1353–1367; Siberian Math. J., 55:6 (2014), 1105–1115
V. I. Murashko, “On partially conjugate-permutable subgroups of finite groups”, PFMT, 2013, no. 1(14), 74–78
Presentations in Math-Net.Ru
1.
On the $\mathfrak{F}$-hypercentral subgroups with ordered Sylow tower of finite groups V. I. Murashka XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich May 30, 2018 17:30
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