Título: Strong conciseness of words in profinite groups

Palestrante: Pavel Shumyatsky (UnB)

 

Abstract: Given a group G and a group-word w, we write w(G) for the verbal subgroup of G corresponding to the word w.
The word is called strongly concise if w(G) is finite for any profinite group G having less than continuously many w-values.

There are substantial reasons to believe that all words are strongly concise. After a brief introduction to this subject I will present a proof of the following theorem:
"Let G be a profinite group admitting a word map w such that there are less than continuously many w-values in G. Then w(w(G)) is finite."