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- W3204102964 abstract "Abstract Let G be a finite transitive group on a set $Omega $ , let $alpha in Omega $ , and let $G_{alpha }$ be the stabilizer of the point $alpha $ in G . In this paper, we are interested in the proportion $$ begin{align*} frac{|{omegain Omegamid omega textrm{ lies in a }G_{alpha}textrm{-orbit of cardinality at most 2}}|}{|Omega|}, end{align*} $$ that is, the proportion of elements of $Omega $ lying in a suborbit of cardinality at most 2. We show that, if this proportion is greater than $5/6$ , then each element of $Omega $ lies in a suborbit of cardinality at most 2, and hence G is classified by a result of Bergman and Lenstra. We also classify the permutation groups attaining the bound $5/6$ . We use these results to answer a question concerning the enumeration of Cayley graphs. Given a transitive group G containing a regular subgroup R , we determine an upper bound on the number of Cayley graphs on R containing G in their automorphism groups." @default.
- W3204102964 created "2021-10-11" @default.
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- W3204102964 date "2023-01-30" @default.
- W3204102964 modified "2023-10-05" @default.
- W3204102964 title "Finite transitive groups having many suborbits of cardinality at most 2 and an application to the enumeration of Cayley graphs" @default.
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- W3204102964 doi "https://doi.org/10.4153/s0008414x23000093" @default.
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