منابع مشابه
On Dense Free Subgroups of Lie Groups
We give a method for constructing dense and free subgroups in real Lie groups. In particular we show that any dense subgroup of a connected semisimple real Lie group G contains a free group on two generators which is still dense in G, and that any finitely generated dense subgroup in a connected non-solvable Lie group H contains a dense free subgroup of rank ≤ 2 · dimH . As an application, we o...
متن کاملCharacterizing Subgroups of Compact Abelian Groups
We prove that every countable subgroup of a compact metrizable abelian group has a characterizing set. As an application, we answer several questions on maximally almost periodic (MAP) groups and give a characterization of the class of (necessarily MAP) abelian topological groups whose Bohr topology has countable pseudocharacter.
متن کاملConjugately Dense Subgroups in Generalized Fc-groups
A subgroup H of a group G is called conjugately dense in G if H has nonempty intersection with each class of conjugate elements in G. The knowledge of conjugately dense subgroups is related with an unsolved problem in group theory, as testified in the Kourovka Notebook. Here we point out the role of conjugately dense subgroups in generalized FC-groups, generalized soluble groups and generalized...
متن کاملEquidistribution of Dense Subgroups on Nilpotent Lie Groups
Let Γ be a dense subgroup of a simply connected nilpotent Lie group G generated by a finite symmetric set S. We consider the n-ball Sn for the word metric induced by S on Γ. We show that Sn (with uniform measure) becomes equidistributed on G with respect to the Haar measure as n tends to infinity. We also prove the analogous result for random walk averages.
متن کاملArithmetically defined dense subgroups of Morava stabilizer groups
For every prime p and integer n > 3 we explicitly construct an abelian variety A/Fpn of dimension n such that for a suitable prime l the group of quasi-isogenies of A/Fpn of l-power degree is canonically a dense subgroup of the n-th Morava stabilizer group at p. We also give a variant of this result taking into account a polarization. This is motivated by the recent construction of topological ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.2307/2038014