Most primitive groups have messy invariants
نویسندگان
چکیده
منابع مشابه
Primitive Monodromy Groups of Genus at most Two
Let X be a compact, connected Riemann surface of genus g, and let ρ : X → P (C) be a covering map of degree N . Then the monodromy group Mon(X, ρ) acts transitively on the fibre of a generic point. Such a group has genus g. We are concerned with the following question. Given an abstract finite group G and a non-negative integer g, does G arise as a monodromy group of genus g? The focus in the p...
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The operation of switching a graph Γ with respect to a subset X of the vertex set interchanges edges and non-edges between X and its complement, leaving the rest of the graph unchanged. This is an equivalence relation on the set of graphs on a given vertex set, so we can talk about the automorphism group of a switching class of graphs. It might be thought that switching classes with many automo...
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We prove that, for a primitive permutation group G acting on a set X of size n, other than the alternating group, the probability that Aut(X, Y ) = G for a random subset Y of X, tends to 1 as n → ∞. So the property of the title holds for all primitive groups except the alternating groups and finitely many others. This answers a question of M. H. Klin. Moreover, we give an upper bound n for the ...
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For a finite group $G$, let $Cent(G)$ denote the set of centralizers of single elements of $G$. In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent, then $Gcong S_3, D_{10}$ or $S_3times S_3$. This result gives a partial and positive answer to a conjecture raised by A. R. Ashrafi [On finite groups with a given number of centralizers, Algebra Collo...
متن کاملCountable Primitive Groups
We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a special case Kleinian groups as well as subgroups of word hyperbolic groups. As an application we calculate the Frattini subgroup in many of these settings, oft...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1979
ISSN: 0001-8708
DOI: 10.1016/0001-8708(79)90038-0