4 papers · 1 filter
On finite-by-nilpotent groups
Eloisa Detomi, Guram Donadze, Marta Morigi +1
Let be the th lower central word. Denote by the set of -values in a group and suppose that there is a number such that …
Strong conciseness in profinite groups
Eloisa Detomi, Benjamin Klopsch, Pavel Shumyatsky
A group word is said to be strongly concise in a class of profinite groups if, for every group in such that takes less than v…
Words of Engel type are concise in residually finite groups. Part II
Eloisa Detomi, Marta Morigi, Pavel Shumyatsky
Given a group-word w and a group G, the verbal subgroup w(G) is the one generated by all w-values in G. The word w is called concise if w(G) is finite whenever the set of w-values…
Profinite groups with restricted centralizers of commutators
E. Detomi, M. Morigi, P. Shumyatsky
A group G has restricted centralizers if for each g in G the centralizer C_G(g) either is finite or has finite index in G. A theorem of Shalev states that a profinite group with re…