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Large free subgroups of automorphism groups of ultrahomogeneous spaces

Szymon Głąb, Filip Strobin (2015)

Colloquium Mathematicae

We consider the following notion of largeness for subgroups of S . A group G is large if it contains a free subgroup on generators. We give a necessary condition for a countable structure A to have a large group Aut(A) of automorphisms. It turns out that any countable free subgroup of S can be extended to a large free subgroup of S , and, under Martin’s Axiom, any free subgroup of S of cardinality less than can also be extended to a large free subgroup of S . Finally, if Gₙ are countable groups, then...

Large superdecomposable E(R)-algebras

Laszlo Fuchs, Rüdiger Göbel (2005)

Fundamenta Mathematicae

For many domains R (including all Dedekind domains of characteristic 0 that are not fields or complete discrete valuation domains) we construct arbitrarily large superdecomposable R-algebras A that are at the same time E(R)-algebras. Here "superdecomposable" means that A admits no (directly) indecomposable R-algebra summands ≠ 0 and "E(R)-algebra" refers to the property that every R-endomorphism of the R-module, A is multiplication by an element of, A.

Large-scale isoperimetry on locally compact groups and applications

Romain Tessera (2006/2007)

Séminaire de théorie spectrale et géométrie

We introduce various notions of large-scale isoperimetric profile on a locally compact, compactly generated amenable group. These asymptotic quantities provide measurements of the degree of amenability of the group. We are particularly interested in a class of groups with exponential volume growth which are the most amenable possible in that sense. We show that these groups share various interesting properties such as the speed of on-diagonal decay of random walks, the vanishing of the reduced first...

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