# zbMATH — the first resource for mathematics

Group structure in finite coverings of compact solenoidal groups. (English) Zbl 0968.22002
It is shown that for any $$n$$-fold covering $$p:X\to G$$ of a compact solenoidal group $$G$$ by a connected topological space $$X$$ the space $$X$$ admits a compatible topological group structure turning $$p$$ into a homomorphism between compact Abelian groups. A topological group $$G$$ is solenoidal provided it admits a continuous group homomorphism $$h:\mathbb R\to G$$ from the additive group of real numbers whose image $$h(\mathbb R)$$ is dense in $$G$$.

##### MSC:
 22A05 Structure of general topological groups 57M10 Covering spaces and low-dimensional topology
##### Keywords:
solenoidal group; covering; topological group structure
Full Text: