This Habilitation thesis is a collection of former research of K. Ersoy. In Chapter
1, Introduction, an outline of his research program in general is given.
• Chapter 2 is the paper of Ersoy, “Infinite Groups with an Anticentral
Element”, [Ers12], appeared in Comm. Alg. 2012.
• Chapter 3 is the paper of Ersoy, “Finite Groups with a Splitting Automor-
phism of Odd Order”, [Ers16], appeared in Arch. Math. 2016.
• Chapter 4 is the paper of Ersoy together with C.K. Gupta, with name “Locally
Finite Groups with Centralizers of Finite Rank”, [EG], appeared in Comm.
• Chapter 5 is the paper of Ersoy together with M. Kuzucuoğlu and P. Shumy-
atsky, with name “Locally Finite Groups and Their Subgroups with Small
Centralizers”, [EKS], appeared in J. Algebra, 2017.
• Chapter 6 is the paper of Ersoy, “Centralizers of p-subgroups in Simple
Locally Finite Groups”, [Ers19], that appeared in Glasgow Mathematical
• Chapter 7 is the paper of Ersoy, together with A. Tortora and M. Tota,
with name “On groups with all subgroups subnormal or soluble of bounded
derived length”, [ETT], appeared in Glasgow Math. J., 2014