On groups where the twisted conjugacy class of the unit element is a subgroup

Author(s)

Goncalves, Daciberg Lima ^[1] ; Nasybullov, Timur ^[2]

Affiliation

^[1] Univ Sao Paulo, Dept Math IME, Sao Paulo - Brazil

^[2] KU Leuven KULAK, Dept Math, Etienne Sabbelaan 53, B-8500 Kortrijk - Belgium

• Document type: Journal article
• Source: COMMUNICATIONS IN ALGEBRA; v. 47, n. 3, p. 930-944, MAR 4 2019.
• Web of Science Citations: 0

Abstract

We study groups G where the -conjugacy class of the unit element is a subgroup of G for every automorphism of G. If G has n generators, then we prove that the k-th member of the lower central series has a finite verbal width bounded in terms of n, k. Moreover, we prove that if such group G satisfies the descending chain condition for normal subgroups, then G is nilpotent, what generalizes the result from {[}Bardakov, Nasybullov, and Neshchadim]. Finally, if G is a finite abelian-by-cyclic group, we construct a good upper bound of the nilpotency class of G. (AU)

• FAPESP's process: 12/24454-8 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants