Carter Subgroups, Amalgams, Simple Groups, and the Zp*-theorem

TL;DR

This paper investigates the structure of a complex group amalgam built from fusion systems at different odd primes, revealing the existence of specific cyclic subgroups and isolated elements, advancing understanding of simple groups.

Contribution

It introduces a novel amalgam construction combining fusion systems for different primes and analyzes its subgroup structure and properties.

Findings

Contains a self-normalizing cyclic subgroup of order pq

Features isolated elements of order p and q

Provides new insights into the structure of amalgams in simple groups

Abstract

We consider an amalgam of groups constructed from fusion systems for different odd primes p and q. This amalgam contains a self-normalizing cyclic subgroup of order pq and isolated elements of order p and q.