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Derangements in finite classical groups for actions related to extension field and imprimitive subgroups and the solution of the Boston-Shalev conjecture
- Publication Year :
- 2015
-
Abstract
- This is the fourth paper in a series. We prove a conjecture made independently by Boston et al and Shalev. The conjecture asserts that there is an absolute positive constant delta such that if G is a finite simple group acting transitively on a set of size n > 1, then the proportion of derangements in G is greater than delta. We show that with possibly finitely many exceptions, one can take delta = .016. Indeed, we prove much stronger results showing that for many actions, the proportion of derangements goes to 1 as n increases and prove similar results for families of permutation representations.<br />Comment: 24 pages
- Subjects :
- Mathematics - Group Theory
Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1508.00039
- Document Type :
- Working Paper