On Root-class Residuality of Generalized Free Products
نویسنده
چکیده
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.
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