Set-stabilizers in solvable permutation groups
Abstract
Let πΊ be a finite solvable permutation group. Then, modulo a possibly trivial normal elementary abelian 3-subgroup, some set-stabilizer in πΊ is a 2-group.
Dedicated to the memory of Marty Isaacs
Acknowledgements
I thank Luca Sabatini for helpful communications.
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Communicated by: Michael Giudici
References
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Solvable and nilpotent subgroups of
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Articles in the same Issue
- Frontmatter
- Bounding the degree of generic sharp transitivity
- Structure of an exotic 2-local subgroup in πΈ7(π)
- Set-stabilizers in solvable permutation groups
- Regular saturated formations of finite soluble groups
- On the π-length and π-class of a π-solvable finite group
- Finite 2-groups with exactly three automorphism orbits
- Finite class 2 nilpotent and Heisenberg groups
- Minimal degrees for faithful permutation representations of groups of order π5 where π is an odd prime
- π-Tilting finiteness of group algebras of semidirect products of abelian π-groups and abelian πβ²-groups
- On the Grossman representations of the automorphism groups of free groups
- Strong indecomposability of the outer automorphism groups of nonabelian free profinite groups
- The proper geometric dimension of the mapping class group of an orientable surface with punctures
- A note on complex hyperbolic lattices and strict hyperbolization
Articles in the same Issue
- Frontmatter
- Bounding the degree of generic sharp transitivity
- Structure of an exotic 2-local subgroup in πΈ7(π)
- Set-stabilizers in solvable permutation groups
- Regular saturated formations of finite soluble groups
- On the π-length and π-class of a π-solvable finite group
- Finite 2-groups with exactly three automorphism orbits
- Finite class 2 nilpotent and Heisenberg groups
- Minimal degrees for faithful permutation representations of groups of order π5 where π is an odd prime
- π-Tilting finiteness of group algebras of semidirect products of abelian π-groups and abelian πβ²-groups
- On the Grossman representations of the automorphism groups of free groups
- Strong indecomposability of the outer automorphism groups of nonabelian free profinite groups
- The proper geometric dimension of the mapping class group of an orientable surface with punctures
- A note on complex hyperbolic lattices and strict hyperbolization
