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L -groups versus k -groups

Roman Frič (1993)

Mathematica Bohemica

We investigate free groups over sequential spaces. In particular, we show that the free k -group and the free sequential group over a sequential space with unique limits coincide and, barred the trivial case, their sequential order is ω 1 .

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...

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