Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

The primitive $p$-Frobenius groups

Author(s): P. Fleischmann; W. Lempken; Pham Huu Tiep
Journal: Proc. Amer. Math. Soc. 126 (1998), 1337-1343.
MSC (1991): Primary 20B15
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Let $p$ be a fixed prime. A finite primitive permutation group $G$ with every two-point stabilizer $G_{\alpha,\beta}$ being a $p$-group is called a primitive $p$-Frobenius group. Using our earlier results on $p$-intersection subgroups, we give a complete classification of the primitive $p$-Frobenius groups.

References:

1.
B. Baumann, Endliche nichtauflösbare Gruppen mit einer nilpotenten maximalen Untergruppe, J. Algebra 38 $(1976)$, $119 - 135$. MR 53:13391

2.
P. Fleischmann, W. Lempken and P.H. Tiep, Finite $p'$-semiregular groups, J. Algebra 188 $(1997)$, $547 - 579$. CMP 97:08

3.
P. Fleischmann, W. Lempken and P.H. Tiep, The $p$-intersection subgroups in quasi-simple and almost simple finite groups, submitted.

4.
D. Gorenstein, ``Finite Groups'', Harper and Row, 1968. MR 38:229

5.
R. Guralnick and R. Wiegand, Galois groups and the multiplicative structure of field extensions, Trans. Amer. Math. Soc. 331 $(1992)$, $563 - 584$. MR 93c:12004

6.
B. Huppert, ``Endliche Gruppen'', Springer, 1967. MR 37:302

7.
M. Liebeck, C. Praeger and J. Saxl, On the O'Nan-Scott theorem for finite primitive permutation groups, J. Austral. Math. Soc. (A) 44 $(1988)$, $389-396$. MR 89a:20002

8.
L. L. Scott, Representations in characteristic $p$, Santa Cruz Conference on Finite Groups, pp. $318 - 331$, Proc. Sympos. Pure Math., vol. 37, Amer. Math. Soc., Providence, R.I., $1980$. MR 82e:20052

9.
H. Zassenhaus, Über endliche Fastkörper, Abhandl. Math. Sem. Hamburg. Univ. 11 $(1936)$, 187-220.

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20B15

Retrieve articles in all Journals with MSC (1991): 20B15

Additional Information:

P. Fleischmann
Affiliation: Institute for Experimental Mathematics, University of Essen, Ellernstr. 29, 45326 Essen, Germany

W. Lempken
Affiliation: Institute for Experimental Mathematics, University of Essen, Ellernstr. 29, 45326 Essen, Germany

Pham Huu Tiep
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Email: tiep@math.ohio-state.edu

DOI: 10.1090/S0002-9939-98-04491-8
PII: S 0002-9939(98)04491-8
Received by editor(s): June 19, 1996
Received by editor(s) in revised form: November 5, 1996
Communicated by: Ronald M. Solomon
Copyright of article: Copyright 1998, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google