Cyclic by prime fixed point free action
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- by Alexandre Turull PDF
- Proc. Amer. Math. Soc. 125 (1997), 3465-3470 Request permission
Abstract:
Let the finite group $A$ be acting on a (solvable) group $G$ and suppose that no non-trivial element of $G$ is fixed under the action of all the elements of $A$. Assume furthermore that $(|A| , |G|) = 1$. A long standing conjecture is that then the Fitting height of $G$ is bounded by the length of the longest chain of subgroups of $A$. Even though this conjecture is known to hold for large classes of groups $A$, it is still unknown for some relatively uncomplicated groups. In the present paper we prove the conjecture for all finite groups $A$ that have a normal cyclic subgroup of square free order and prime index. Since many of these groups have natural modules where they act faithfully and coprimely but without regular orbits, the result is new for many of the groups we consider.References
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Additional Information
- Alexandre Turull
- Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
- Email: turull@math.ufl.edu
- Received by editor(s): June 11, 1996
- Additional Notes: Partially supported by a grant from the NSF
- Communicated by: Ronald M. Solomon
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 3465-3470
- MSC (1991): Primary 20D45
- DOI: https://doi.org/10.1090/S0002-9939-97-04263-9
- MathSciNet review: 1443859