Voir la notice de l'article provenant de la source Math-Net.Ru
@article{IVM_2023_4_a6,
author = {N. Yang and N. N. Vorob'ev and I. I. Staselka},
title = {On modularity and algebraicity of the lattice of multiply $\omega$-composition {Fitting} classes},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {76--88},
publisher = {mathdoc},
number = {4},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2023_4_a6/}
}
TY - JOUR AU - N. Yang AU - N. N. Vorob'ev AU - I. I. Staselka TI - On modularity and algebraicity of the lattice of multiply $\omega$-composition Fitting classes JO - Izvestiâ vysših učebnyh zavedenij. Matematika PY - 2023 SP - 76 EP - 88 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IVM_2023_4_a6/ LA - ru ID - IVM_2023_4_a6 ER -
%0 Journal Article %A N. Yang %A N. N. Vorob'ev %A I. I. Staselka %T On modularity and algebraicity of the lattice of multiply $\omega$-composition Fitting classes %J Izvestiâ vysših učebnyh zavedenij. Matematika %D 2023 %P 76-88 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/IVM_2023_4_a6/ %G ru %F IVM_2023_4_a6
N. Yang; N. N. Vorob'ev; I. I. Staselka. On modularity and algebraicity of the lattice of multiply $\omega$-composition Fitting classes. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2023), pp. 76-88. http://geodesic.mathdoc.fr/item/IVM_2023_4_a6/
[1] Shemetkov L.A., Formatsii konechnykh grupp, Sovrem. algebra, Nauka, M., 1978 | MR
[2] Shemetkov L.A., Skiba A.N., Formatsii algebraicheskikh sistem, Sovrem. algebra, Nauka, M., 1989 | MR
[3] Doerk K., Hawkes T.O., Finite Soluble Groups, De Gruyter Expo. Math., 4, De Gruyter, Berlin–New York, 1992 | MR | Zbl
[4] Skiba A.N., Algebra formatsii, Belaruskaya navuka, Minsk, 1997 | MR
[5] Guo W., The Theory of Classes of Groups, Mathematics and Its Applications, 505, Science Press / Kluwer Academic Publishers, Beijing–New York–Dordrecht–Boston–London, 2000 | MR | Zbl
[6] Ballester-Bolinches A., Ezquerro L.M., Classes of Finite Groups, Mathematics and Its Applications, 584, Springer, Dordrecht, 2006 | MR | Zbl
[7] Monakhov V.S., Vvedenie v teoriyu konechnykh grupp i ikh klassov, ucheb. posobie, Vysh. shk., Minsk, 2006
[8] Guo W., Structure Theory for Canonical Classes of Finite Groups, Springer, Berlin, 2015 | MR | Zbl
[9] Skiba A.N., Shemetkov L.A., “Kratno $\omega$-lokalnye formatsii i klassy Fittinga konechnykh grupp”, Matem. tr., 2:2 (1999), 114–147 | MR | Zbl
[10] Skiba A.N., Shemetkov L.A., “Kratno $\mathfrak{L}$-kompozitsionnye formatsii konechnykh grupp”, Ukrainsk. matem. zhurn., 52:6 (2000), 783–797 | MR | Zbl
[11] Vedernikov V.A., Sorokina M.M., “$\Omega$-rassloennye formatsii i klassy Fittinga konechnykh grupp”, Diskretn. matem., 13:3 (2001), 125–144 | DOI | Zbl
[12] Yang N., Vorob'ev N.N., Filimonova A.R., “On the modularity property of the lattice of partially composition Fitting classes”, Rend. Semin. Mat. Univ. Padova, 146 (2021), 43–55 | DOI | MR
[13] Vorobev N.T., “O predpolozhenii Khouksa dlya radikalnykh klassov”, Sib. matem. zhurn., 37:6 (1996), 1296–1302 | MR | Zbl
[14] Salii V.N., Reshetki s edinstvennymi dopolneniyami, Sovrem. algebra, Nauka, M., 1984
[15] Skiba A.N., “O lokalnykh formatsiyakh dliny $5$”, Arifmeticheskoe i podgruppovoe stroenie konechnykh grupp, Nauka i tekhn., Minsk, 1986, 135–149
[16] Vorobev N.N., Algebra klassov konechnykh grupp, VGU im. P.M. Masherova, Vitebsk, 2012
[17] Ballester-Bolinches A., Shemetkov L.A., “On Lattices of $p$-Local Formations of Finite Groups”, Math. Nachr., 186:1 (1997), 57–65 | DOI | MR | Zbl
[18] Chi Z., Safonov V.G., Skiba A.N., “On $n$-multiply $\sigma$-local formations of finite groups”, Comm. Algebra, 47:3 (2019), 957–968 | DOI | MR | Zbl
[19] Reifferscheid S., “A note on subgroup-closed Fitting classes of finite soluble groups”, J. Group Theory, 6:3 (2003), 331–345 | DOI | MR | Zbl
[20] Safonov V.G., “On a question of the theory of totally saturated formations of finite groups”, Algebra Colloq., 15:1 (2008), 119–128 | DOI | MR | Zbl
[21] Safonov V.G., “On modularity of the lattice of totally saturated formations of finite groups”, Comm. Algebra, 35:11 (2007), 3495–3502 | DOI | MR | Zbl
[22] Shabalina I.P., “O reshetke $\tau$-zamknutykh $n$-kratno $\omega$-lokalnykh formatsii konechnykh grupp”, Vestsi NAN Belarusi, Ser. fiz.-matem. navuk, 2003, no. 1, 28–30 | MR
[23] Scherbina V.V., Safonov V.G., “O podreshetkakh reshetki chastichno totalno nasyschennykh formatsii konechnykh grupp”, Nauchn. vedomosti BelGU. Ser. Matem. i Fizika, 51:1 (2019), 64–87
[24] Scherbina V.V., Safonov V.G., “O nekotorykh svoistvakh reshetki chastichno totalno nasyschennykh formatsii konechnykh grupp”, Nauchn. vedomosti BelGU. Ser. Matem. i Fizika, 51:2 (2019), 227–244
[25] Shemetkov L.A., Skiba A.N., Vorob'ev N.N., “On lattices of formations of finite groups”, Algebra Colloq., 17:4 (2010), 557–564 | DOI | MR | Zbl
[26] Shemetkov L.A., Skiba A.N., Vorob'ev N.N., “On laws of lattices of partially saturated formations”, Asian-Eur. J. Math., 2:1 (2009), 155–169 | DOI | MR | Zbl
[27] Tsarev A.A., “On the lattice of all totally composition formations of finite groups”, Ric. Mat., 68:2 (2019), 693–698 | DOI | MR | Zbl
[28] Tsarev A.A., Vorob'ev N.N., “Lattices of composition formations of finite groups and the laws”, J. Algebra Appl. and Appl., 17:5 (2018), 1850084-1–1850084-17 | DOI | MR
[29] Tsarev A.A., Vorob'ev N.N., “On a question of the theory of partially composition formations”, Algebra Colloq., 21:3 (2014), 437–447 | DOI | MR | Zbl
[30] Vorobev N.N., Skiba A.N., “O distributivnosti reshetki razreshimykh totalno lokalnykh klassov Fittinga”, Matem. zametki, 67:5 (2000), 662–673 | DOI | MR | Zbl
[31] Vorobev N.N., Skiba A.N., Tsarev A.A., “Tozhdestva reshetok chastichno kompozitsionnykh formatsii”, Sib. matem. zhurn., 52:5 (2011), 1011–1024 | MR | Zbl
[32] Vorobev N.N., Tsarev A.A., “O modulyarnosti reshetki $\tau$-zamknutykh $n$-kratno $\omega$-kompozitsionnykh formatsii”, Ukrainsk. matem. zhurn., 62:4 (2010), 453–463 | MR | Zbl
[33] Zhiznevskii P.A., “O modulyarnosti i induktivnosti reshetki vsekh $\tau$-zamknutykh $n$-kratno $\omega$-kompozitsionnykh formatsii konechnykh grupp”, Izv. Gomelsk. gos. un-ta im. F. Skoriny, 2010, no. 1, 185–191 | Zbl
[34] Unsolved Problems in Group Theory, The Kourovka Notebook, 20, Russian Acad. Sci., Siberian Branch, Univ. Lincoln, Sobolev Inst. Math., Novosibirsk, 2022
[35] Artamonov V.A., Salii V.N., Skornyakov L.A. i dr., Obschaya algebra, v. 2, Sprav. matem. b-ka, ed. Skornyakov L.A., Nauka, M., 1991 | MR
[36] Tsarev A.A., “Algebraic lattices of partially saturated formations of finite groups”, Afr. Mat., 31:3–4 (2020), 701–707 | DOI | MR | Zbl
[37] Safonov V.G., “Ob algebraichnosti reshetki $\tau$-zamknutykh totalno nasyschennykh formatsii”, Algebra i logika, 45:5 (2006), 620–626 | MR | Zbl
[38] Shabalina I.P., “Algebraichnost reshetki $\tau$-zamknutykh $n$-kratno $\omega$-lokalnykh formatsii”, Izv. Gomelsk. gos. un-ta im. F. Skoriny, 2002, no. 1, Voprosy algebry–18, 59–67 | Zbl
[39] Scherbina V.V., “Algebraichnost reshetki $\tau$-zamknutykh totalno $\omega$-nasyschennykh formatsii konechnykh grupp”, Ufimsk. matem. zhurn., 12:1 (2020), 83–91
[40] Tsarev A.A., Kukharev A.V., “Algebraic lattices of solvably saturated formations and their applications”, Bol. Soc. Mat. Mex. III, 26:3 (2020), 1003–1014 | DOI | MR | Zbl
[41] Scherbina V.V., “O dvukh zadachakh teorii chastichno totalno kompozitsionnykh formatsii konechnykh grupp”, Prikl. matem. fizika, 52:1 (2020), 18–32 | DOI
[42] Kamozina O.V., “O neodnoporozhdennykh kratno $\omega$-veernykh klassakh Fittinga konechnykh grupp”, Matem. zametki, 79:3 (2006), 396–408 | DOI | MR | Zbl
[43] Kamozina O.V., “Algebraicheskie reshetki kratno $\Omega$-rassloennykh klassov Fittinga”, Diskret. matem., 18:2 (2006), 139–145 | DOI | MR | Zbl
[44] Kamornikov S.F., Shemetkov L.A., “O koradikalakh subnormalnykh podgrupp”, Algebra i logika, 34:5 (1995), 493–513 | MR | Zbl