On the Residual Finiteness of Certain Polygonal Products

Abstract

AbstractWe give examples to show that unlike generalized free products of groups (g.f.p.) polygonal products of finitely generated (f.g.) nilpotent groups with cyclic amalgamations need not be residually finite (R) and polygonal products of finite p-groups with cyclic amalgamations need not be residually nilpotent. However, polygonal products f.g. abelian groups are R, and under certain conditions polygonal products of finite p-groups with cyclic amalgamations are R.