Algorithms for permutability in finite groups

Adolfo Ballester-Bolinches; Enric Cosme-Llópez; Ramón Esteban-Romero

Open Mathematics (2013)

  • Volume: 11, Issue: 11, page 1914-1922
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Adolfo Ballester-Bolinches, Enric Cosme-Llópez, and Ramón Esteban-Romero. "Algorithms for permutability in finite groups." Open Mathematics 11.11 (2013): 1914-1922. <http://eudml.org/doc/269091>.

@article{AdolfoBallester2013,
abstract = {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.},
author = {Adolfo Ballester-Bolinches, Enric Cosme-Llópez, Ramón Esteban-Romero},
journal = {Open Mathematics},
keywords = {Finite group; Permutable subgroup; S-permutable subgroup; Dedekind group; Iwasawa group; T-group; PT-group; PST-group; Algorithm; finite groups; permutability properties; algorithms; permutable subgroups; Sylow-permutable subgroups; finite T-groups; PT-groups; PST-groups},
language = {eng},
number = {11},
pages = {1914-1922},
title = {Algorithms for permutability in finite groups},
url = {http://eudml.org/doc/269091},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Adolfo Ballester-Bolinches
AU - Enric Cosme-Llópez
AU - Ramón Esteban-Romero
TI - Algorithms for permutability in finite groups
JO - Open Mathematics
PY - 2013
VL - 11
IS - 11
SP - 1914
EP - 1922
AB - 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.
LA - eng
KW - Finite group; Permutable subgroup; S-permutable subgroup; Dedekind group; Iwasawa group; T-group; PT-group; PST-group; Algorithm; finite groups; permutability properties; algorithms; permutable subgroups; Sylow-permutable subgroups; finite T-groups; PT-groups; PST-groups
UR - http://eudml.org/doc/269091
ER -

References

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  1. [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 Zbl1182.20024
  2. [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 Zbl1033.20019
  3. [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 Zbl1041.20013
  4. [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. [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 Zbl0999.20012
  6. [6] Ballester-Bolinches A., Esteban-Romero R., Asaad M., Products of Finite Groups, de Gruyter Exp. Math., 53, Walter de Gruyter, Berlin, 2010 http://dx.doi.org/10.1515/9783110220612 Zbl1206.20019
  7. [7] Ballester-Bolinches A., Esteban-Romero R., Ragland M., A note on finite PST-groups, J. Group Theory, 2007, 10(2), 205–210 http://dx.doi.org/10.1515/JGT.2007.016 Zbl1120.20023
  8. [8] Ballester-Bolinches A., Esteban-Romero R., Ragland M., Corrigendum: A note on finite PST-groups, J. Group Theory, 2009, 12(6), 961–963 http://dx.doi.org/10.1515/JGT.2009.026 Zbl1183.20018
  9. [9] Beidleman J.C., Brewster B., Robinson D.J.S., Criteria for permutability to be transitive in finite groups, J. Algebra, 1999, 222(2), 400–412 http://dx.doi.org/10.1006/jabr.1998.7964 
  10. [10] Beidleman J.C., Heineken H., Finite soluble groups whose subnormal subgroups permute with certain classes of subgroups, J. Group Theory, 2003, 6(2), 139–158 http://dx.doi.org/10.1515/jgth.2003.010 Zbl1045.20012
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  13. [13] Robinson D.J.S., A note on finite groups in which normality is transitive, Proc. Amer. Math. Soc., 1968, 19(4), 933–937 http://dx.doi.org/10.1090/S0002-9939-1968-0230808-9 Zbl0159.31002
  14. [14] Schmid P., Subgroups permutable with all Sylow subgroups, J. Algebra, 1998, 207(1), 285–293 http://dx.doi.org/10.1006/jabr.1998.7429 
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