Infinite simple groups with no proper abnormal subgroups

TL;DR

This paper constructs infinite simple groups with no proper abnormal subgroups, answering longstanding open problems and demonstrating new properties of such groups using an embedding theorem.

Contribution

It introduces a novel construction of infinite simple groups with specific subgroup properties, solving open problems in group theory.

Findings

Constructed infinite simple groups with no proper abnormal subgroups

Provided affirmative answer to Revin's problem

Offered negative answer to a question by Kurdachenko, Russo, and Vincenzi

Abstract

Utilizing an embedding theorem of Obraztsov we construct groups as described in the title. This provides an affirmative answer to a problem of D. O. Revin. The constructed groups also provide a negative answer to a question highlighted by Kurdachenko, Russo, and Vincenzi.