{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/32245"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/32245","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Frobenius transfers and p-local finite groups","abstract":"In this thesis we explore the possibility of defining the p-local finite groups of Broto, Levi and Oliver in terms of their classifying spaces. More precisely, we consider the question posed by Haynes Miller, whether an equivalent theory can be recovered by studying maps f: BS --> X from the classifying space of a finite p-group S to a p-complete space X equipped with a stable retract t satisfying a form of Frobenius reciprocity. In the case where S is elementary abelian, we answer this question in the affirmative, by showing that under some finiteness conditions such a triple (f, t, X) does indeed induce a p-local finite group over S. We also discuss the converse in some detail for general S.","abstract_html":"In this thesis we explore the possibility of defining the p-local finite groups of Broto, Levi and Oliver in terms of their classifying spaces. More precisely, we consider the question posed by Haynes Miller, whether an equivalent theory can be recovered by studying maps f: BS --> X from the classifying space of a finite p-group S to a p-complete space X equipped with a stable retract t satisfying a form of Frobenius reciprocity. In the case where S is elementary abelian, we answer this question in the affirmative, by showing that under some finiteness conditions such a triple (f, t, X) does indeed induce a p-local finite group over S. We also discuss the converse in some detail for general S.","abstract_has_math":false,"creators":["Ragnarsson, KaÅ i, 1977-"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Haynes R. Miller."],"committee_chairs":[],"committee_members":[],"year":2004,"date_issued":"2004","date_published":"2004","updated_at":"2026-07-22T22:20:53Z","subjects":["Mathematics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. 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More precisely, we consider the question posed by Haynes Miller, whether an equivalent theory can be recovered by studying maps f: BS --> X from the classifying space of a finite p-group S to a p-complete space X equipped with a stable retract t satisfying a form of Frobenius reciprocity. In the case where S is elementary abelian, we answer this question in the affirmative, by showing that under some finiteness conditions such a triple (f, t, X) does indeed induce a p-local finite group over S. We also discuss the converse in some detail for general S."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Frobenius transfers and p-local finite groups"]}]}],"canonical_facts":{"dc:contributor.advisor":["Haynes R. Miller."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:creator":["Ragnarsson, KaÅ i, 1977-"],"dc:date.accessioned":["2006-03-29T18:27:18Z"],"dc:date.available":["2006-03-29T18:27:18Z"],"dc:date.issued":["2004"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.","Includes bibliographical references (p. 43-44)."],"dc:description.abstract":["In this thesis we explore the possibility of defining the p-local finite groups of Broto, Levi and Oliver in terms of their classifying spaces. More precisely, we consider the question posed by Haynes Miller, whether an equivalent theory can be recovered by studying maps f: BS --> X from the classifying space of a finite p-group S to a p-complete space X equipped with a stable retract t satisfying a form of Frobenius reciprocity. In the case where S is elementary abelian, we answer this question in the affirmative, by showing that under some finiteness conditions such a triple (f, t, X) does indeed induce a p-local finite group over S. We also discuss the converse in some detail for general S."],"dc:description.degree":["Ph.D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/1721.1/32245"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["Frobenius transfers and p-local finite groups"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:20:53Z"}