Geodesic
Pro-$p$ Groups with Finite Number of Ends
Matematičeskie zametki, Tome 76 (2004) no. 4, pp. 531-538

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The number of ends for a pro-p group is defined. The adequacy of the definition is confirmed by the obtained pro-p analogs of results on the number of ends of abstract groups. In particular, it is shown that, as in the abstract case, a pro-p group can have only 0, 1, 2, or infinitely many ends; pro-p groups with two ends are classified and a sufficient condition for a pro-p group to have precisely one end is obtained. 
@article{MZM_2004_76_4_a5,
     author = {A. A. Korenev},
     title = {Pro-$p$ {Groups} with {Finite} {Number} of {Ends}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {531--538},
     publisher = {mathdoc},
     volume = {76},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a5/}
}
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A. A. Korenev. Pro-$p$ Groups with Finite Number of Ends. Matematičeskie zametki, Tome 76 (2004) no. 4, pp. 531-538. http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a5/