A note on barely transitive permutation groups satisfying
Constructing a maximal cofinitary group.
Die harmonischen Involutionen der Permutationsgruppe P...L2 (K).
Examples of non-shy sets
Christensen has defined a generalization of the property of being of Haar measure zero to subsets of (abelian) Polish groups which need not be locally compact; a recent paper of Hunt, Sauer, and Yorke defines the same property for Borel subsets of linear spaces, and gives a number of examples and applications. The latter authors use the term “shyness” for this property, and “prevalence” for the complementary property. In the present paper, we construct a number of examples of non-shy Borel sets...
Malnormal subgroups and Frobenius groups: basics and examples
Malnormal subgroups occur in various contexts. We review a large number of examples, and compare the general situation to that of finite Frobenius groups of permutations.In a companion paper [18], we analyse when peripheral subgroups of knot groups and -manifold groups are malnormal.
Modular permutations on
Monochrome symmetric subsets in 2-colorings of groups.
On certain characterizations of barely transitive groups
On locally graded barely transitive groups
We show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup 〈x〉 which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H 1 of finite index in H satisfying the identity χ(H 1) = 1, where χ is a multi-linear commutator of weight w.
On locally graded non-periodic barely transitive groups
Orbite di gruppi di permutazioni infiniti
Possible cardinalities of maximal abelian subgroups of quotients of permutation groups of the integers
If G is a group then the abelian subgroup spectrum of G is defined to be the set of all κ such that there is a maximal abelian subgroup of G of size κ. The cardinal invariant A(G) is defined to be the least uncountable cardinal in the abelian subgroup spectrum of G. The value of A(G) is examined for various groups G which are quotients of certain permutation groups on the integers. An important special case, to which much of the paper is devoted, is the quotient of the full symmetric group by the...
Relatively Homogeneous Locally Finite Permutation Groups.
Sequences realized as Parker vectors of oligomorphic permutation groups.
Sui vettori di Parker e concetti correlati
The permutation group induced on a moiety.
The prevalence of permutations with infinite cycles
A number of recent papers have been devoted to the study of prevalence, a generalization of the property of being of full Haar measure to topological groups which need not have a Haar measure, and the dual concept of shyness. These concepts give a notion of "largeness" which often differs from the category analogue, comeagerness, and may be closer to the intuitive notion of "almost everywhere." In this paper, we consider the group of permutations of natural numbers. Here, in the sense of category,...
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