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Results tagged with gr.group-theory
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user 171304
Questions about the branch of algebra that deals with groups.
10
votes
1
answer
320
views
Do these properties of a countable abelian group guarantee a Prüfer subgroup?
Suppose $(G,+)$ is a countable abelian group and $p$ is a prime number such that:
The subgroup $pG$ has finite index in $G$, and
For every $n \in \mathbb{N}$, $G$ contains an element of order $p^n$.
…
- 198
6
votes
0
answers
91
views
Does every compact abelian group contain a Kronecker set generating a dense subgroup?
Let $G$ be a compact metrizable abelian group with infinite exponent.
Let $S^1 = \left\{z \in \mathbb{C} : |z| = 1 \right\}$. A set $K \subset G$ is a Kronecker set if, for every continuous function $ …
- 198
2
votes
Accepted
Density of “diagonal sets” in amenable groups
The answer to your question as stated is "no", but a variant of it is true (see the proposition below).
Proof that the answer is "no": Let $(F_n)$ be the Følner sequence in $\mathbb{Z}$ given by $F_n …
- 198