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INTERSECTIONS OF ODD ORDER HALL SUBGROUPS

Published online by Cambridge University Press:  08 February 2005

SILVIO DOLFI
SILVIO DOLFI
Affiliation:
Dipartimento di Matematica, viale Morgagni, 67/a, 50134 Firenze, [email protected]
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Abstract

Given a set $\pi$ of odd primes and a $\pi$-solvable finite group $G$, one can choose three (not necessarily distinct) Hall $\pi$-subgroups of $G$ whose intersection is $O_{\pi}(G)$. This statement relies on a result concerning long orbits in coprime actions of groups of odd order.

Keywords

20D20
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 1 , January 2005 , pp. 61 - 66
Copyright
© The London Mathematical Society 2005

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Footnotes

Work partially supported by MURST research program ‘Teoria dei gruppi e applicazioni’.