Large free subgroups of automorphism groups of ultrahomogeneous spaces
Szymon Głąb ; Filip Strobin
Colloquium Mathematicae, Tome 139 (2015), p. 279-295 / Harvested from The Polish Digital Mathematics Library
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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 either ∏n∈ℕGₙ is large, or it does not contain any free subgroup on uncountably many generators.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:284204 
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Szymon Głąb; Filip Strobin. Large free subgroups of automorphism groups of ultrahomogeneous spaces. Colloquium Mathematicae, Tome 139 (2015) pp. 279-295. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-2-7/