Abstract: | We study into widths of verbal subgroups of HNN-extensions, and of groups with one defining relation. It is proved that if
a group G* is an HNN-extension and the connected subgroups in G* are distinct from a base of the extension, then every verbal subgroup V(G*) has infinite width relative to a finite proper set V of words. A similar statement is proven to hold for groups presented
by one defining relation and ≥3 generators.
to Yurii I. Merzlyakov dedicated
Supported by RFFR grant No. 93-01-01513.
Translated fromAlgebra i Logika, Vol. 36, No. 5, pp. 494–517, September–October, 1997. |