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On the size of the nilpotent residual in finite groups
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S Dolfi
Published/Copyright:
June 18, 2007
Abstract
Let G be a finite non-abelian group satisfying Φ(G) = 1 and denote by U the nilpotent residual of G. In this paper, we prove that if G is of odd order then 
, and if G is of even order not divisible by a Mersenne or a Fermat prime then 
. These results are best possible and the assumption Φ(G) = 1 cannot be omitted.
Received: 2006-07-05
Revised: 2006-09-13
Published Online: 2007-06-18
Published in Print: 2007-05-23
© Walter de Gruyter
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Articles in the same Issue
- Transitivity properties for group actions on buildings
- Fields, values and character extensions in finite groups
- Primitive sharp permutation groups with large solvable subgroups
- On the size of the nilpotent residual in finite groups
- On the commuting complex of finite metanilpotent groups
- Soluble normally constrained pro-p-groups
- Comparing quasi-finitely axiomatizable and prime groups
- A finitely presented torsion-free simple group
- Andrews–Curtis groups and the Andrews–Curtis conjecture
- Residual finiteness of outer automorphism groups of certain tree products
- Commutator subgroups of Hantzsche–Wendt groups
