Let G be a finite transitive group of rank r. We give a short proof that the proportion of derangements in G is at most 1 - 1/r and we classify the permutation groups attaining this bound.
Guralnick, R., Isaacs, I., Spiga, P. (2015). On a relation between the rank and the proportion of derangements in finite transitive permutation groups. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 136, 198-200 [10.1016/j.jcta.2015.07.003].
On a relation between the rank and the proportion of derangements in finite transitive permutation groups
SPIGA, PABLOUltimo
2015
Abstract
Let G be a finite transitive group of rank r. We give a short proof that the proportion of derangements in G is at most 1 - 1/r and we classify the permutation groups attaining this bound.
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