Pronormal and subnormal subgroups and permutability

James Beidleman; Hermann Heineken

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 3, page 605-615
  • ISSN: 0392-4041

Abstract

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We describe the finite groups satisfying one of the following conditions: all maximal subgroups permute with all subnormal subgroups, (2) all maximal subgroups and all Sylow p -subgroups for p < 7 permute with all subnormal subgroups.

How to cite

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Beidleman, James, and Heineken, Hermann. "Pronormal and subnormal subgroups and permutability." Bollettino dell'Unione Matematica Italiana 6-B.3 (2003): 605-615. <http://eudml.org/doc/195659>.

@article{Beidleman2003,
abstract = {We describe the finite groups satisfying one of the following conditions: all maximal subgroups permute with all subnormal subgroups, (2) all maximal subgroups and all Sylow $p$-subgroups for $p< 7$ permute with all subnormal subgroups.},
author = {Beidleman, James, Heineken, Hermann},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {finite groups; subnormal subgroups; maximal subgroups; Frattini quotient groups; polycyclic groups; pronormal subgroups},
language = {eng},
month = {10},
number = {3},
pages = {605-615},
publisher = {Unione Matematica Italiana},
title = {Pronormal and subnormal subgroups and permutability},
url = {http://eudml.org/doc/195659},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Beidleman, James
AU - Heineken, Hermann
TI - Pronormal and subnormal subgroups and permutability
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/10//
PB - Unione Matematica Italiana
VL - 6-B
IS - 3
SP - 605
EP - 615
AB - We describe the finite groups satisfying one of the following conditions: all maximal subgroups permute with all subnormal subgroups, (2) all maximal subgroups and all Sylow $p$-subgroups for $p< 7$ permute with all subnormal subgroups.
LA - eng
KW - finite groups; subnormal subgroups; maximal subgroups; Frattini quotient groups; polycyclic groups; pronormal subgroups
UR - http://eudml.org/doc/195659
ER -

References

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  1. AGRAWAL, R. K., Finite groups whose subnormal subgroups permute with all Sylow subgroups, Proc. Amer. Math. Soc., 47 (1975), 77-83. Zbl0299.20014MR364444
  2. ALEJANDRE, M.- BALLESTER-BOLINCHES, A.- PEDRAZA-AGUILERA, M. C., Finite Soluble Groups with Permutable Subnormal Subgroups, J. Algebra, 240 (2001), 705-722. Zbl0983.20014MR1841353
  3. BAER, R.Überauflösbare Gruppen, Abh. Math. Sem. Univ. Hamburg, 23(1959), 11-28. Zbl0092.02004MR103925
  4. BEIDLEMAN, J. C.- BREWSTER, B.- ROBINSON, D. J. S., Criteria for permutability to be transitive in finite groups, J. Algebra, 222 (1999), 400-412. Zbl0948.20015MR1733679
  5. BEIDLEMAN, J. C.- HEINEKEN, H., Finite Soluble Groups Whose Subnormal Subgroups Permute With Certain Classes of Subgroups, J. Group Theory (to appear). Zbl1045.20012
  6. CONWAY, J. H.- CURTISS, R. T.- NORTON, S. P.- PARKER, R. A.- WILSON, R. A., Atlas of finite groups, Clarendon Press, Oxford, 1985. Zbl0568.20001MR827219
  7. BRYCE, R. A.- COSSEY, J., The Wielandt subgroup of a finite soluble group, J. London Math. Soc., 40 (1989), 244-256. Zbl0734.20010MR1044272
  8. GASCHÜTZ, W., Gruppen, in denen das Normalteilersein transitivist, J. reine angew Math., 198 (1957), 87-92. Zbl0077.25003MR91277
  9. GORENSTEIN, D., Finite Simple Groups, Plenum Press, New York and London, 1982. Zbl0483.20008MR698782
  10. HUPPERT, B., Normalteiler und maximale Untergruppen endlicher Gruppen, Math. Z., 60 (1954), 409-434. Zbl0057.25303MR64771
  11. KEGEL, O. H., Sylow-Gruppen und Subnormalteiler endlicher Gruppen, Math. Z., 78 (1962), 205-221. Zbl0102.26802MR147527
  12. MAIER, R., Zur Vertauschbarkeit und Subnormalität von Untergruppen, Arch. Math., 53 (1989), 110-120. Zbl0673.20012MR1004266
  13. PENG, T. A., Finite groups with pronormal subgroups, Proc. Amer. Math. Soc., 20 (1969), 232-234. Zbl0167.02302MR232850
  14. ROBINSON, D. J. S., A note on finite groups in which normality is transitive, Proc. Amer. Math. Soc., 19 (1968), 933-937. Zbl0159.31002MR230808
  15. ROBINSON, D. J. S., A survey of groups in which normality or permutability is transitive, (Indian National Science Academy, New Delhi1999), 171-181. Zbl0952.20017MR1690796
  16. ROBINSON, D. J. S., The Structure of Finite Groups in which Permutability is a Transitive Relation, J. Austral. Math. Soc., 70 (2001), 143-159. Zbl0997.20027MR1815277
  17. ZACHER, G., I gruppi risolubili finiti in cui i sottogruppi di composizione coincidano con i sottogruppi quasi-normali, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 37 (1964), 150-154. Zbl0136.28302MR174633

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