Finite groups with primitive Sylow normalizers
D'Aniello, A. ; De Vivo, C. ; Giordano, G.
Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002), p. 235-245 / Harvested from Biblioteca Digitale Italiana di Matematica
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We prove that are primitive the finite groups whose normalizers of the Sylow subgroups are primitive. We classify the groups of such class, denoted by N⁢P, and we study the Schunck classes whose boundary is contained in N⁢P. We give also necessary and sufficient conditions in order that the projectors be subnormally embedded.

Si prova che sono primitivi i gruppi finiti nei quali siano primitivi i normalizzanti dei sottogruppi di Sylow. Si classificano i gruppi di tale classe, denotata con N⁢P, e si studiano le classi di Schunck il cui bordo sia contenuto in N⁢P, fornendo, tra l'altro, condizioni necessarie e sufficienti affinchè i proiettori siano subnormalmente immersi.

Publié le : 2002-02-01
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     author = {A. D'Aniello and C. De Vivo and G. Giordano},
     title = {Finite groups with primitive Sylow normalizers},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {5-A},
     year = {2002},
     pages = {235-245},
     zbl = {1072.20026},
     mrnumber = {1881934},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2002_8_5B_1_235_0}
}

D'Aniello, A.; De Vivo, C.; Giordano, G. Finite groups with primitive Sylow normalizers. Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002) pp. 235-245. http://gdmltest.u-ga.fr/item/BUMI_2002_8_5B_1_235_0/

[1] Ballester-Bolinches, A., Characterizations of Schunck classes of finite soluble groups, J. Algebra, 202 (1998), 243-249. | MR 1614210 | Zbl 0914.20018

[2] Ballester-Bolinches, A.-Shemetkov, L. A., On normalizers of Sylow subgroups in finite groups, Sib. Math. Journal, to appear. | MR 1686994 | Zbl 0941.20015

[3] Bianchi, M. G.-Gillio Berta Mauri, A.-Hauck, P., On finite groups with nilpotent Sylow normalizers, Arch. Math., 47 (1986), 193-197. | MR 861865 | Zbl 0605.20017

[4] Blessenohl, D.-Gaschütz, W., Über normale Schunck und Fittingklassen, Math. Z., 118 (1970), 1-8. | MR 277611 | Zbl 0208.03301

[5] Bryce, R. A.-Fedri, V.-Serena, L., Bounds on the Fitting length of finite soluble groups with supersoluble Sylow normalizers, Bull. Austral. Math. Soc., 44 (1991), 19-31. | MR 1120390 | Zbl 0719.20009

[6] Doerk, K.-Hawkes, T., Finite soluble groups, W. de Gruyter, Berlin (1992). | MR 1169099 | Zbl 0753.20001

[7] Fedri, V.-Serena, L., Finite soluble groups with supersoluble Sylow normalizers, Arch. Math., 50 (1988), 11-18. | MR 925488 | Zbl 0638.20013

[8] Förster, P., Projektive Klassen endlicher Gruppen I, Schunck und Gaschützklassen, Math. Z., 186 (1984), 248-278. | MR 741300 | Zbl 0544.20015

[9] Glauberman, G., Prime-power factor groups of finite groups II, Math. Z., 117 (1970), 46-56. | MR 294483 | Zbl 0192.35501

[10] Gorenstein, D., Finite Groups, Harper and Row, New York (1968). | MR 231903 | Zbl 0185.05701

[11] Huppert, B., Endliche Gruppen I, Springer-Verlag, Berlin (1969). | MR 224703 | Zbl 0217.07201

[12] Huppert, B.-Blackburn, N., Finite groups II, Springer-Verlag, Berlin (1982). | MR 650245 | Zbl 0477.20001