2004/08/20 by D. N. Azarov, D. Tieudjo
Mathematics · #math.GR #msc:20E06 #msc:20E26 #msc:20F05 #msc:20F19
published as Nauch. Trudy IvGU, vol. 5, 2002, p.6-10 (in Russian) · 6 pages
arxiv created 2004/08/20 · arxiv updated 2009/12/01
Root-class residuality of free product of root-class residual groups is demonstrated. A sufficient condition for root-class residuality of generalized free product G of groups A and B amalgamating subgroups H and K through the isomorphism ϕ is derived. For the particular case when A=B, H=K and ϕ is the identity mapping, it is shown that group G is root-class residual if and only if A is root-class residual and subgroup H of A is root-class closed. These results are extended to generalized free product of infinitely many groups amalgamating a common subgroup.