Geodesic
Group structure in finite coverings of compact solenoidal groups
Lobachevskii journal of mathematics, Tome 6 (2000), pp. 39-46.

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Let $p\colon X\to G$ be an $n$-fold covering of a compact solenoidal group $G$ by a connected topological space $X$. We prove that there exists a group structure in $X$ turning $p$ into a homomorphism between compact abelian groups. 
@article{LJM_2000_6_a3,
     author = {S. A. Grigoryan and R. N. Gumerov and A. V. Kazantsev},
     title = {Group structure in finite coverings of compact solenoidal groups},
     journal = {Lobachevskii journal of mathematics},
     pages = {39--46},
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     volume = {6},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2000_6_a3/}
}
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S. A. Grigoryan; R. N. Gumerov; A. V. Kazantsev. Group structure in finite coverings of compact solenoidal groups. Lobachevskii journal of mathematics, Tome 6 (2000), pp. 39-46. http://geodesic.mathdoc.fr/item/LJM_2000_6_a3/