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Bulletin of the London Mathematical Society 2005 37(1):61-66; doi:10.1112/S0024609304003807
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© London Mathematical Society

Intersections of Odd Order Hall Subgroups

Silvio Dolfi

Dipartimento di Matematica, viale Morgagni 67/a, 50134 Firenze, Italy; dolfi{at}math.unifi.it

Received 1 April 2003. Revision received 17 December 2003.

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. 2000 Mathematics Subject Classification 20D20.

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


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