Prasma, Matan and Schlank, Tomer M. (2017) Sylow theorems for infinity-groups. TOPOLOGY AND ITS APPLICATIONS, 222. pp. 121-138. ISSN 0166-8641, 1879-3207
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Viewing Kan complexes as infinity-groupoids implies that pointed and connected Kan complexes are to be viewed as infinity-groups. A fundamental question is then: to what extent can one "do group theory" with these objects? In this paper we develop a notion of a finite infinity-group: an infinity-group whose homotopy groups are all finite. We prove a homotopical analogue of Sylow theorems for finite infinity-groups. This theorem has two corollaries: the first is a homotopical analogue of Burnside's fixed point lemma for p-groups and the second is a "group-theoretic" characterisation of finite nilpotent spaces. (C) 2017 Elsevier B.V. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; infinity-group; Sylow subgroup; k-invariant; infinity-category |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Alexander Schmidt |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:10 |
| Last Modified: | 15 Feb 2019 12:29 |
| URI: | https://pred.uni-regensburg.de/id/eprint/884 |
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