Varieties of groups and the problem on conciseness of words

Seminario del Dipartimento di Matematica
25 June 2024
Start time 
4:00 pm
Polo Ferrari 1 - Via Sommarive 5, Povo (Trento)
Room A107
Dipartimento di Matematica
Target audience: 
University community
UniTrento students
Contact person: 
Prof. Willem Adriaan De Graaf, dott.ssa Mima Stanojkovski
Contact details: 
Staff Dipartimento di Matematica
Cristina Acciarri (Università di Modena e Reggio Emilia)


A group-word w is said to be concise if whenever the set of w-values in a group G is finite it always follows that the verbal subgroup w(G) is finite. More generally, a word w is called concise in a class of groups X if whenever the set of w-values is finite for a group G belonging to the class X, it always follows that w(G) is finite. P. Hall asked whether every word is concise. Due to S. Ivanov the answer to this problem is known to be negative. On the other hand, for residually finite groups the problem remains wide open. Our talk will be about recent developments with respect to that problem. Based on a joint work with P. Shumyatsky (University of Brasilia).