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On pro-S groups
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Liad Fireman
Published/Copyright:
April 23, 2010
Abstract
Let S be a finite simple group, and 
the class of poly-S groups, that is, finite groups with all composition factors isomorphic to S. A pro-S group is defined to be an inverse limit of poly-S groups. If S = Cp, the finite cyclic group of order p, we get the familiar pro-p groups. We study the case when S is non-abelian, and particularly the structure of free and projective pro-S groups and their subgroups. We show that pro-S groups have a rich structure, and that the categories of pro-p and pro-S groups are very different.
Received: 2008-02-08
Revised: 2009-10-10
Published Online: 2010-04-23
Published in Print: 2010-September
© de Gruyter 2010
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- A classification of certain finite double coset collections in the exceptional groups
- Recognizing SL2(q) in fusion systems
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Articles in the same Issue
- On triangle generation of finite groups of Lie type
- Hurwitz generation of the universal covering of Alt(n)
- A classification of certain finite double coset collections in the exceptional groups
- Recognizing SL2(q) in fusion systems
- Complete LR-structures on solvable Lie algebras
- Involutions and free pairs of bicyclic units in integral group rings
- Hypercentral groups with all subgroups subnormal
- On pro-S groups
- On groups acting on contractible spaces with stabilizers of prime-power order
