Formations of finite groups in polynomial time: : F-residuals and F-subnormality
References
[1]
Adolfo Ballester-Bolinches, Enric Cosme-Llópez, Ramón Esteban-Romero, GAP package permut — a package to deal with permutability in finite groups, v. 2.0.3, 2018, 2014.
[2]
L. Babai, On the length of subgroup chains in the symmetric group, Commun. Algebra 14 (1986) 1729–1736.
[3]
L. Babai, E.M. Luks, A. Seress, Permutations groups in NC, in: Proc. 19th ACM STOC, 1987, pp. 409–420.
[4]
A. Ballester-Bolinches, E. Cosme-Llópez, R. Esteban-Romero, Algorithms for permutability in finite groups, Cent. Eur. J. Math. 11 (2013) 1914–1922.
[5]
A. Ballester-Bolinches, R. Esteban-Romero, M. Asaad, Products of Finite Groups, De Gruyter, 2010.
[6]
A. Ballester-Bolinches, L.M. Ezquerro, Classes of Finite Groups, Math. Appl., vol. 584, Springer Netherlands, 2006.
[7]
K. Doerk, T.O. Hawkes, Finite Soluble Groups, De Gruyter Exp. Math., vol. 4, De Gruyter, Berlin, New York, 1992.
[8]
B. Eick, C.R. Wright, GAP package FORMAT — computing with formations of finite solvable groups, v.1.4.3, 2020, 2000.
[9]
B. Eick, C.R. Wright, Computing subgroups by exhibition in finite solvable groups, J. Symb. Comput. 33 (2002) 129–143.
[10]
W. Guo, Structure Theory for Canonical Classes of Finite Groups, Springer-Verlag, Berlin, Heidelberg, 2015.
[11]
W. Guo, A.N. Skiba, On finite quasi-F-groups, Commun. Algebra 37 (2009) 470–481.
[12]
W. Guo, A.N. Skiba, On some classes of finite quasi-F-groups, J. Group Theory 12 (2009) 407–417.
[13]
T. Hawkes, On formation subgroups of a finite soluble group, J. Lond. Math. Soc. s1–44 (1969) 243–250.
[14]
B. Höfling, GAP package CRISP — computing with Radicals, Injectors, Schunck classes and Projectors, v. 1.4.5, 2019, 2000.
[15]
B. Höfling, Computing projectors, injectors, residuals and radicals of finite soluble groups, J. Symb. Comput. 32 (2001) 499–511.
[16]
B. Huppert, N. Blackburn, Finite Groups II, Grundlehren der mathematischen Wissenschaften, Springer, Berlin, Heidelberg, 1982.
[17]
W.M. Kantor, Sylow's theorem in polynomial time, J. Comput. Syst. Sci. 30 (1985) 359–394.
[18]
W.M. Kantor, Finding Sylow normalizers in polynomial time, J. Algorithms 11 (1990) 523–563.
[19]
W.M. Kantor, E.M. Luks, Computing in quotient groups, in: Proceedings of the Twenty–Second Annual ACM Symposium on Theory of Computing, Baltimore, May 14–16, ACM, New York, 1990, pp. 524–534.
[20]
O.H. Kegel, Untergruppenverbände endlicher Gruppen, die den Subnormalteilerverband echt enthalten, Arch. Math. 30 (1978) 225–228.
[21]
V.S. Monakhov, Finite groups with a given set of Schmidt subgroups, Math. Notes 58 (1995) 1183–1186.
[22]
V.S. Monakhov, Three formations over U, Math. Notes 110 (2021) 339–346.
[23]
V.S. Monakhov, I.L. Sokhor, On groups with formational subnormal Sylow subgroups, J. Group Theory 21 (2018) 273–287.
[24]
V.I. Murashka, Finite groups with given sets of F-subnormal subgroups, Asian-Eur. J. Math. 13 (2018).
[25]
L. Rónyai, Computing the structure of finite algebras, J. Symb. Comput. 9 (1990) 355–373.
[26]
V.N. Semenchuk, S.N. Shevchuk, Characterization of classes of finite groups with the use of generalized subnormal Sylow subgroups, Math. Notes 89 (2011) 117–120.
[27]
Á. Seress, Permutation Group Algorithms, Cambridge University Press, Cambridge, 2003.
[28]
L.A. Shemetkov, Formations of Finite Groups, Nauka, Moscow, 1978, in Russian.
[29]
A.F. Vasil'ev, T.I. Vasil'eva, V.N. Tyutyanov, On the finite groups of supersoluble type, Sib. Math. J. 51 (2010) 1004–1012.
[30]
A.F. Vasil'ev, T.I. Vasil'eva, A.S. Vegera, Finite groups with generalized subnormal embedding of Sylow subgroups, Sib. Math. J. 57 (2016) 200–212.
[31]
V.A. Vasilyev, Finite groups with submodular Sylow subgroups, Sib. Math. J. 56 (2015) 1019–1027.
[32]
zbMATH Open (2023): Papers with classification 20D10. https://www.zbmath.org/?au=&ti=&so=&la=&py=&ab=&rv=&an=&en=&cc=20D10&ut=&sw=&br=&any=&dm=&dt=j.
[33]
I. Zimmermann, Submodular subgroups in finite groups, Math. Z. 202 (1989) 545–557.
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Published: 14 March 2024
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