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Number of Sylow subgroups in $p$-solvable groups


Author: Gabriel Navarro
Journal: Proc. Amer. Math. Soc. 131 (2003), 3019-3020
MSC (2000): Primary 20D20
Published electronically: March 11, 2003
MathSciNet review: 1993207
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Abstract: If $G$ is a finite group and $p$ is a prime number, let $\nu_p(G)$be the number of Sylow $p$-subgroups of $G$. If $H$ is a subgroup of a $p$-solvable group $G$, we prove that $\nu_p(H)$ divides $\nu_p(G)$.


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Additional Information

Gabriel Navarro
Affiliation: Departament d’Àlgebra, Facultat de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain
Email: gabriel@uv.es

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06884-9
Received by editor(s): April 25, 2002
Received by editor(s) in revised form: May 13, 2002
Published electronically: March 11, 2003
Additional Notes: The author’s research was partially supported by DGICYT
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2003 American Mathematical Society