Lifting in Frattini covers and a characterization of finite solvable groups
-
Robert M. Guralnick
and
Pham Huu Tiep
Abstract
We prove a lifting theorem for odd Frattini covers of finite groups. Using this, we generalize a result of J. G. Thompson and characterize finite solvable groups as those finite groups which do not contain nontrivial elements xi, i = 1,2,3, with x1x2x3 = 1 and xi a pi-element for distinct primes pi. We note some connections with coverings of curves.
Funding source: NSF
Award Identifier / Grant number: DMS-1001962
Funding source: NSF
Award Identifier / Grant number: DMS-0901241
Funding source: NSF
Award Identifier / Grant number: DMS-1201374
Funding source: Simons Foundation
Award Identifier / Grant number: 224965
Funding source: Institute for Advanced Study
The authors are grateful to the referees and to Pierre Dèbes, Michael Fried, David Harbater and Gunter Malle for their careful reading and helpful comments on the paper.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- The length metric on the set of orthogonal projections and new estimates in the subspace perturbation problem
- A Giambelli formula for even orthogonal Grassmannians
- Lifting in Frattini covers and a characterization of finite solvable groups
- Note on basic features of large time behaviour of heat kernels
- A decomposition theorem in II1-factors
- Wonderful resolutions and categorical crepant resolutions of singularities
- Tannaka–Kreĭn duality for compact quantum homogeneous spaces II. Classification of quantum homogeneous spaces for quantum SU(2)
- An approach of the minimal model program for horospherical varieties via moment polytopes
- Height of exceptional collections and Hochschild cohomology of quasiphantom categories
Articles in the same Issue
- Frontmatter
- The length metric on the set of orthogonal projections and new estimates in the subspace perturbation problem
- A Giambelli formula for even orthogonal Grassmannians
- Lifting in Frattini covers and a characterization of finite solvable groups
- Note on basic features of large time behaviour of heat kernels
- A decomposition theorem in II1-factors
- Wonderful resolutions and categorical crepant resolutions of singularities
- Tannaka–Kreĭn duality for compact quantum homogeneous spaces II. Classification of quantum homogeneous spaces for quantum SU(2)
- An approach of the minimal model program for horospherical varieties via moment polytopes
- Height of exceptional collections and Hochschild cohomology of quasiphantom categories
