Finite groups with primitive Sylow normalizers

A. D'Aniello; C. De Vivo; G. Giordano

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 1, page 235-245
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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D'Aniello, A., De Vivo, C., and Giordano, G.. "Finite groups with primitive Sylow normalizers." Bollettino dell'Unione Matematica Italiana 5-B.1 (2002): 235-245. <http://eudml.org/doc/195467>.

@article{DAniello2002,
abstract = {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 $N\mathcal\{P\}$, and we study the Schunck classes whose boundary is contained in $N\mathcal\{P\}$. We give also necessary and sufficient conditions in order that the projectors be subnormally embedded.},
author = {D'Aniello, A., De Vivo, C., Giordano, G.},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {Sylow subgroups; normalizers; homomorphs; Schunck classes; boundaries},
language = {eng},
month = {2},
number = {1},
pages = {235-245},
publisher = {Unione Matematica Italiana},
title = {Finite groups with primitive Sylow normalizers},
url = {http://eudml.org/doc/195467},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - D'Aniello, A.
AU - De Vivo, C.
AU - Giordano, G.
TI - Finite groups with primitive Sylow normalizers
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/2//
PB - Unione Matematica Italiana
VL - 5-B
IS - 1
SP - 235
EP - 245
AB - 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 $N\mathcal{P}$, and we study the Schunck classes whose boundary is contained in $N\mathcal{P}$. We give also necessary and sufficient conditions in order that the projectors be subnormally embedded.
LA - eng
KW - Sylow subgroups; normalizers; homomorphs; Schunck classes; boundaries
UR - http://eudml.org/doc/195467
ER -

References

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  1. BALLESTER-BOLINCHES, A., Characterizations of Schunck classes of finite soluble groups, J. Algebra, 202 (1998), 243-249. Zbl0914.20018MR1614210
  2. BALLESTER-BOLINCHES, A.- SHEMETKOV, L. A., On normalizers of Sylow subgroups in finite groups, Sib. Math. Journal, to appear. Zbl0941.20015MR1686994
  3. BIANCHI, M. G.- GILLIO BERTA MAURI, A.- HAUCK, P., On finite groups with nilpotent Sylow normalizers, Arch. Math., 47 (1986), 193-197. Zbl0605.20017MR861865
  4. BLESSENOHL, D.- GASCHÜTZ, W., Über normale Schunck und Fittingklassen, Math. Z., 118 (1970), 1-8. Zbl0208.03301MR277611
  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. Zbl0719.20009MR1120390
  6. DOERK, K.- HAWKES, T., Finite soluble groups, W. de Gruyter, Berlin (1992). Zbl0753.20001MR1169099
  7. FEDRI, V.- SERENA, L., Finite soluble groups with supersoluble Sylow normalizers, Arch. Math., 50 (1988), 11-18. Zbl0638.20013MR925488
  8. FÖRSTER, P., Projektive Klassen endlicher Gruppen I, Schunck und Gaschützklassen, Math. Z., 186 (1984), 248-278. Zbl0544.20015MR741300
  9. GLAUBERMAN, G., Prime-power factor groups of finite groups II, Math. Z., 117 (1970), 46-56. Zbl0192.35501MR294483
  10. GORENSTEIN, D., Finite Groups, Harper and Row, New York (1968). Zbl0185.05701MR231903
  11. HUPPERT, B., Endliche Gruppen I, Springer-Verlag, Berlin (1969). Zbl0217.07201MR224703
  12. HUPPERT, B.- BLACKBURN, N., Finite groups II, Springer-Verlag, Berlin (1982). Zbl0477.20001MR650245

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