Large free subgroups of automorphism groups of ultrahomogeneous spaces

• Autorzy: Szymon Głąb , Filip Strobin
• Języki publikacji: EN

Abstrakty

EN

We consider the following notion of largeness for subgroups of $S_{∞}$. A group G is large if it contains a free subgroup on 𝔠 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 𝔠 can also be extended to a large free subgroup of $S_{∞}$. Finally, if Gₙ are countable groups, then either $∏_{n∈ℕ} Gₙ$ is large, or it does not contain any free subgroup on uncountably many generators.

Kategorie tematyczne

• 20E05: Free nonabelian groups
• 20B27: Infinite automorphism groups
• 54H11: Topological groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 140
• Numer: 2
• Strony: 279-295

Daty

wydano

2015

Twórcy

autor

Szymon Głąb

• Institute of Mathematics, Lodz University of Technology, Wólczańska 215, 93-005 Łódź, Poland

autor

Filip Strobin

• Institute of Mathematics, Lodz University of Technology, Wólczańska 215, 93-005 Łódź, Poland

Identyfikatory

DOI

10.4064/cm140-2-7