N-determined 2-compact groups
Jesper M. M{\o}ller

TL;DR
This paper develops a classification scheme for 2-compact groups using maximal torus normalizer pairs, demonstrating that many are N-determined and confirming a conjecture by Dwyer and Wilkerson.
Contribution
It introduces a general classification framework for 2-compact groups and proves that all connected and some non-connected groups are N-determined, also computing automorphism groups.
Findings
All connected 2-compact groups are N-determined.
Some non-connected 2-compact groups are N-determined.
The splitting conjecture by Dwyer and Wilkerson is confirmed.
Abstract
We first formulate a general scheme for the classification of 2-compact groups in terms of maximal torus normalizer pairs. Applying this scheme, we show that all connected and some non-connected 2-compact groups are N-determined. We also compute automorphism groups in many cases. As an application we confirm the splitting conjecture formulated by Dwyer and Wilkerson.
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Taxonomy
TopicsFinite Group Theory Research · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology
