Prasma, Matan ; Schlank, Tomer M.
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| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Topology and its Applications |
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| Verlag: | ELSEVIER SCIENCE BV |
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| Ort der Veröffentlichung: | AMSTERDAM |
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| Band: | 222 |
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| Seitenbereich: | S. 121-138 |
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| Datum: | 2017 |
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| Institutionen: | Mathematik > Prof. Dr. Alexander Schmidt |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.1016/j.topol.2017.03.004 | DOI |
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| Stichwörter / Keywords: | ; infinity-group; Sylow subgroup; k-invariant; infinity-category |
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| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
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| Status: | Veröffentlicht |
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| Begutachtet: | Ja, diese Version wurde begutachtet |
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| An der Universität Regensburg entstanden: | Ja |
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| Dokumenten-ID: | 39000 |
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Zusammenfassung
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 ...
Zusammenfassung
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.
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