It is [known](https://en.wikipedia.org/wiki/Stallings_theorem_about_ends_of_groups) that the number of ends of a finitely generated group is 0,1, 2 or $\infty$.



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> **Problem 1.** What is known about the number of ends of infinite finitely generated torsion groups?
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In particular,



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> **Problem 2.** Is there any description of finitely generated torsion groups with 1 end?
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Ends of finitely generated torsion groups
Stallings' Theorem, given in his book [Group theory and three-dimensinal manifolds](https://mathscinet.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=ALLF&pg8=ET&review_format=html&s4=stallings&s5=&s6=&s7=three%20dimensional&s8=All&sort=Newest&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=2&mx-pid=415622), states that a f.g. group with 2 or infinitely many ends splits *essentially* as a graph of groups with finite edge groups and therefore, being infinite, acts without fixed points on a simplicial tree, and therefore has an infinite order element.


