Confined subgroups and high transitivity

Topological Transitivity and Strong Transitivity

We discuss the relation between (topological) transitivity and strong transitivity of dynamical systems. We show that a transitive and open self-map of a compact metric space satisfying a certain expanding condition is strongly transitive. We also prove a couple of results for interval maps; for example it is shown that a transitive piecewise monotone interval map is strongly transitive.

On the cut-off phenomenon for the transitivity of randomly generated subgroups

Consider K ≥ 2 independent copies of the random walk on the symmetric group SN starting from the identity and generated by the products of either independent uniform transpositions or independent uniform neighbor transpositions. At any time n ∈ N, let Gn be the subgroup of SN generated by the K positions of the chains. In the uniform transposition model, we prove that there is a cut-off phenome...

The Equivalence of High Subgroups

Two subgroups of a group G are called equivalent if there is an automorphism of G that maps one of the subgroups onto the other. Suppose that G is a /7-primary abelian group and that A is an ordinal. A subgroup H oî G is //-high in G if H is maximal in G with respect to having zero intersection with p G. Under certain conditions on the quotient group G/pxG slightly weaker than total projectivit...

Truth-Grounding and Transitivity

It is argued that if we take grounding to be univocal, then there is a serious tension between truthgrounding and one commonly assumed structural principle for grounding, namely transitivity. The primary claim of the paper is that truth-grounding cannot be transitive. Accordingly, it is either the case that grounding is not transitive or that truth-grounding is not grounding, or both.

Grounding, transitivity, and contrastivity