Groups with Boundedly Finite Conjugacy Classes of Commutators

2017/02/07 by Dierings, Glaucia, Shumyatsky, Pavel · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1702.02224

Abstract

In 1954 B. H. Neumann discovered that if G is a group in which all conjugacy classes are finite with bounded size, then the derived group G' is finite. Later (in 1957) Wiegold found an explicit bound for the order of G'. We study groups in which the conjugacy classes containing commutators are finite with bounded size. We obtain the following results. Let G be a group and n a positive integer. If |x^G|

Cited by

• On Chernikov-by-nilpotent groups

Related

• On finite groups with bounded conjugacy classes of commutators
• Bounded conjugacy classes, commutators, and approximate subgroups
• BFC-theorems for higher commutator subgroups
• Multiplicities of conjugacy class sizes of finite groups
• Finite groups have even more conjugacy classes