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 A-family and show that any simple 2-compact group that is locally isomorphic to PGL(n+1,ℂ) is uniquely N-determined. Thus there are no other 2-compact groups in the A-family than the ones we already know. We also compute the group of automorphisms of any member of the A-family and show that it consists of unstable Adams operations only.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm195-1-2,
author = {Jesper M. M\o ller},
title = {N-determined 2-compact groups. I},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {11-84},
zbl = {1136.55006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm195-1-2}
}
Jesper M. Møller. N-determined 2-compact groups. I. Fundamenta Mathematicae, Tome 193 (2007) pp. 11-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm195-1-2/