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Sylow permutable subnormal subgroups of finite groups II

Published online by Cambridge University Press:  17 April 2009

A. Ballester-Bolinches  and
R. Esteban-Romero
A. Ballester-Bolinches
Affiliation:
Departament d'Àlgebra, Universitat de València, Dr. Moliner, 50, E–46100 Burjassot (València), Spain e-mail: Adolfo.Ballester@uv.es
R. Esteban-Romero
Affiliation:
Departament de Matemàtica Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, E–46022 València, Spain e-mail: resteban@mat.upv.es
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Abstract

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In this paper a local version of Agrawal's theorem about the structure of finite groups in which Sylow permutability is transitive is given. The result is used to obtain new characterisations of this class of finite groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 3 , December 2001 , pp. 479 - 486
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Agrawal, R.K., ‘Finite groups whose subnormal subgroups permute with all Sylow sub-groups’, Proc. Amer. Math. Soc. 47 (1975), 77–83.Google Scholar
[2]Alejandre, M.J., Ballester-Bolinches, A., and Pedraza-Aguilera, M.C., ‘Finite soluble groups with permutable subnormal subgroups’, J. Algebra 240 (2001), 705–722.CrossRefGoogle Scholar
[3]Ballester-Bolinches, A. and Esteban-Romero, R., ‘Sylow permutable subnormal subgroups of finite groups’, preprint.Google Scholar
[4]Beidleman, J.C., Brewster, B., and Robinson, D.J.S., ‘Criteria for permutability to be transitive in finite groups’, J. Algebra 222 (1999), 400–412.CrossRefGoogle Scholar
[5]Beidleman, J.C. and Heineken, H., ‘Finite soluble groups whose subnormal subgroups permute with certain classes of subgroups’, (preprint).Google Scholar
[6]Bryce, R.A. and Cossey, J., ‘The Wielandt subgroup of a finite soluble group’, J. London Math. Soc. 40 (1989), 244–256.CrossRefGoogle Scholar
[7]Doerk, K. and Hawkes, T., Finite soluble groups, de Gruyter Expositions in Mathematics 4 (Walter de Gruyter, Berlin, New York, 1992).Google Scholar
[8]Gaschütz, W., ‘Gruppen, in dennen das Normalteilersein transitiv ist.’, J. Reine Angew. Math. 198 (1957), 87–92.CrossRefGoogle Scholar
[9]Kegel, O.H., ‘Sylow-Gruppen und Subnormalteiler endlicher Gruppen’, Math. Z. 78 (1962), 205–221.Google Scholar
[10]Lennox, J.C. and Stonehewer, S.E., Subnormal subgroups, Oxford Mathematical Monographs (Oxford University Press, New York, 1987).Google Scholar
[11]Robinson, D.J.S., ‘A note on finite groups in which normality is transitive’, Proc. Amer. Math. Soc. 19 (1968), 933–937.CrossRefGoogle Scholar
[12]Schmid, P., ‘Subgroups permutable with all Sylow subgroups’, J. Algebra 207 (1998), 285–293.CrossRefGoogle Scholar
[13]Zacher, G., ‘I gruppi risolubli finiti in cui i sottogruppi di composizione coincidono con i sottogrupi quasi-normali’, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 37 (1964), 150–154.Google Scholar