Algorithms for permutability in finite groups

• Autorzy: Adolfo Ballester-Bolinches , Enric Cosme-Llópez , Ramón Esteban-Romero
• Języki publikacji: EN

Abstrakty

EN

In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.

Słowa kluczowe

EN

Finite group; Permutable subgroup; S-permutable subgroup; Dedekind group; Iwasawa group; T-group; PT-group; PST-group; Algorithm

Kategorie tematyczne

• 20-04: Explicit machine computation and programs (not the theory of computation or programming)
• 20D20: Sylow subgroups, Sylow properties, π -groups, π -structure
• 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, π -length, ranks

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 11
• Strony: 1914-1922

Daty

wydano

2013-11-01

online

2013-08-23

Twórcy

autor

Adolfo Ballester-Bolinches

• Universitat de València

autor

Enric Cosme-Llópez

• Universitat de València

autor

Ramón Esteban-Romero

Bibliografia

• [1] Ballester-Bolinches A., Beidleman J.C., Cossey J., Esteban-Romero R., Ragland M.F., Schmidt J., Permutable subnormal subgroups of finite groups, Arch. Math. (Basel), 2009, 92(6), 549–557 http://dx.doi.org/10.1007/s00013-009-2976-x
• [2] Ballester-Bolinches A., Beidleman J.C., Heineken H., Groups in which Sylow subgroups and subnormal subgroups permute, Illinois J. Math., 2003, 47(1–2), 63–69
• [3] Ballester-Bolinches A., Beidleman J.C., Heineken H., A local approach to certain classes of finite groups, Comm. Algebra, 2003, 31(12), 5931–5942 http://dx.doi.org/10.1081/AGB-120024860
• [4] Ballester-Bolinches A., Cosme-Llópez E., Esteban-Romero R., Permut: A GAP4 package to deal with permutability, v. 0.03, available at http://personales.upv.es/_resteban/gap/permut-0.03/
• [5] Ballester-Bolinches A., Esteban-Romero R., Sylow permutable subnormal subgroups of finite groups, J. Algebra, 2002, 251(2), 727–738 http://dx.doi.org/10.1006/jabr.2001.9138
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Identyfikatory

DOI

10.2478/s11533-013-0299-4