Grupos com classe de conjugação verbal limitada

Abstract

Let F be a free group and let w F. For a group G, we denote the set of all the w-values in G and by w (G) = [Gw] the verbal subgroup of G corresponding to w. A word w is called boundedly concise if, for each group G such that / Gw / n, we have / w (G)/ c, for some integer c depending only on n. We will show w is a word boundedly and G is a group such that / xGw / m for all x G every x then / xw (G) d such that x for every x G, and a some interger d= d(m,w) depending only on m and w.