A fruitful and active area of modern group theory is called geometric group theory, where we study the interplay between algebraic properties and geometric properties of groups. In this thesis, we study two recently introduced geometric properties and make progress in characterizing solvable groups that satisfy these properties. The first property, uniformly almost flatness on the quotients, is related to the research conducted by Khukhro and Valette when they investigated the diameter of the finite quotients of residually finite groups. The second property, conjugacy ratio, was introduced by Ciobanu, Cox and Martino. They studied the quotient of two functions naturally associated with any finitely generated group: conjugacy growth and standard growth.
Some topics related to growth in soluble groups
Guo, D. (Author). 30 Sept 2025
Student thesis: Doctoral Thesis › Doctor of Philosophy (PhD)