2013/08/08 by E. V. Sokolov, Sokolov, E. V.
Mathematics · Social Sciences · #20E06 #20E26 #FOS: Mathematics #Group Theory (math.GR) #Japanese History and Culture #math.GR #msc:20E06 #msc:20E26
paper · pdf · doi:10.48550/arxiv.1308.1976
arxiv created 2013/08/08 · openalex publication_date 2013/08/08 · arxiv updated 2013/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be the free product of groups A and B with commuting subgroups H \leqslant A and K \leqslant B, and let C be the class of all finite groups or the class of all finite p-groups. We derive the description of all C-separable cyclic subgroups of G provided this group is residually a C-group. We prove, in particular, that if A, B are finitely generated nilpotent groups and H, K are p'-isolated in the free factors, then all p'-isolated cyclic subgroups of G are separable in the class of all finite p-groups. The same statement is true provided A, B are free and H, K are p'-isolated and cyclic.