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On formations with the Kegel property
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Published/Copyright:
September 8, 2005
Abstract
We say that a formation ℱ of finite groups has the
Kegel property if ℱ contains every group of the form G = AB = BC = CA with
A, B, C in ℱ. Vasil’ev asked the following
question in the Kourovka Notebook: if ℱ is a soluble Fitting formation of finite
groups with the Kegel property must ℱ be a saturated formation? We obtain an
affirmative answer in the soluble universe in the case when ℱ has the following
additional property: for every prime p ∈ char ℱ and every primitive
ℱ-group G whose socle is a p -group, 
lies in ℱ for all primes q ≠ p
such that q divides |G | Soc(G )|.
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Published Online: 2005-09-08
Published in Print: 2005-09-19
Walter de Gruyter GmbH & Co. KG
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Articles in the same Issue
- Abelian subgroups of small index in finite p-groups
- Non-divisibility among character degrees
- Some remarks on the k(GV ) theorem
- On formations with the Kegel property
- Good tori in groups of finite Morley rank
- The existence of Carter subgroups in groups of finite Morley rank
- Extensions of characters of discrete torsion-free nilpotent groups
- Modules of type FP2 over the integral group algebra of a metabelian group
Articles in the same Issue
- Abelian subgroups of small index in finite p-groups
- Non-divisibility among character degrees
- Some remarks on the k(GV ) theorem
- On formations with the Kegel property
- Good tori in groups of finite Morley rank
- The existence of Carter subgroups in groups of finite Morley rank
- Extensions of characters of discrete torsion-free nilpotent groups
- Modules of type FP2 over the integral group algebra of a metabelian group
