Publishing house / Journals and Serials / Fundamenta Mathematicae / All issues

Abstract

This is the first part of a paper that classifies $2$-compact groups. In this first part we formulate a general classification scheme for $2$-compact groups in terms of their maximal torus normalizer pairs. We apply this general classification procedure to the simple $2$-compact groups of the $\mathrm{A}$-family and show that any simple $2$-compact group that is locally isomorphic to ${\rm PGL}(n+1,{\mathbb C})$ is uniquely $N$-determined. Thus there are no other $2$-compact groups in the $\mathrm{A}$-family than the ones we already know. We also compute the group of automorphisms of any member of the $\mathrm{A}$-family and show that it consists of unstable Adams operations only.