Automorphism Groups of Graph Products of Buildings

TL;DR

This paper investigates the automorphism groups of graph products of buildings, revealing their structure and residual finiteness when buildings are finite, and introduces a generalized graph product concept.

Contribution

It characterizes the automorphism group of graph products of buildings and links generalized graph products to automorphisms generated via lifts, extending understanding of their structure.

Findings

Automorphism group described for graph products of buildings

Generalized graph product corresponds to automorphisms via lifts

Finite buildings imply residual finiteness of the generalized graph product

Abstract

We describe an underlying right angled building structure of any graph product of buildings. We describe the automorphism group of the graph product of buildings. We show that the notion of generalized graph product of a collection of groups, each with an action on a building, corresponds to the group of automorphisms generated via lifts. It follows that if each building is finite, then the generalized graph product is residually finite.