{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/22828"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/22828","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Multiplicity-free permutation representations of the alternating groups","abstract":"A transitive permutation representation of a finite group G is said to be multiplicity-free if each irreducible constituent of the associated permutation character of G occurs with multiplicity one. If H is a subgroup of G, then G acts naturally on the set of cosets of H. This action is transitive and the associated permutation character is given by the character 1$\\rm \\sbsp{H}{G}$ of G induced from the trivial character of H. If 1$\\rm \\sbsp{H}{G}$ is multiplicity-free, then H is said to be a multiplicity-free subgroup of G.","abstract_html":"A transitive permutation representation of a finite group G is said to be multiplicity-free if each irreducible constituent of the associated permutation character of G occurs with multiplicity one. If H is a subgroup of G, then G acts naturally on the set of cosets of H. This action is transitive and the associated permutation character is given by the character 1$\\rm \\sbsp{H}{G}$ of G induced from the trivial character of H. If 1$\\rm \\sbsp{H}{G}$ is multiplicity-free, then H is said to be a multiplicity-free subgroup of G.","abstract_has_math":true,"creators":["Balmaceda, Jose Maria P."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Suzuki, Michio"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:52:50Z","date_published":"2011-05-07T13:52:50Z","updated_at":"2026-07-22T22:25:20Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1991 Balmaceda, Jose Maria P."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9136537","(UMI)AAI9136537"],"render_values":[{"text":"AAI9136537","href":null,"code":true},{"text":"(UMI)AAI9136537","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/22828","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Suzuki, Michio"]},{"key":"dc:creator","label":"Author","values":["Balmaceda, Jose Maria P."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:52:50Z","10000-01-01","1991"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1991 Balmaceda, Jose Maria P."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9136537","(UMI)AAI9136537","http://hdl.handle.net/2142/22828"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A transitive permutation representation of a finite group G is said to be multiplicity-free if each irreducible constituent of the associated permutation character of G occurs with multiplicity one. If H is a subgroup of G, then G acts naturally on the set of cosets of H. This action is transitive and the associated permutation character is given by the character 1$\\rm \\sbsp{H}{G}$ of G induced from the trivial character of H. If 1$\\rm \\sbsp{H}{G}$ is multiplicity-free, then H is said to be a multiplicity-free subgroup of G.","In this paper the multiplicity-free subgroups H of the alternating groups A$\\sb{\\rm n}$, n $>$ 18, are investigated and classified in the main chapter. The key tools involve bounds on the order of H and the analysis of the orbits of H on k-element subsets of the set of n elements on which A$\\sb{\\rm n}$ acts, k $\\leq$ n. The multiplicity-free subgroups of A$\\sb{\\rm n}$ are shown to have large orders and to be highly transitive. Explicit decompositions of several permutation characters are obtained.","A survey of the known results on multiplicity-free permutation representations is included. It is shown that 1$\\rm \\sbsp{H}{G}$ is multiplicity-free if and only if the algebra of complex-valued functions on G which are constant on the (H,H)-double cosets under the convolution product is commutative. The author proves that if G is a group of odd order which admits an involutary automorphism, and H is the subgroup of fixed points, then 1$\\rm \\sbsp{H}{G}$ is multiplicity-free.","Made available in DSpace on 2011-05-07T13:52:50Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9136537.pdf: 2745354 bytes, checksum: 428ac582bf9ed9205e06bd42ec3e23aa (MD5) Previous issue date: 1991","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:00:17Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:28:30-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Multiplicity-free permutation representations of the alternating groups"]}]}],"canonical_facts":{"dc:contributor":["Suzuki, Michio"],"dc:creator":["Balmaceda, Jose Maria P."],"dc:date":["2011-05-07T13:52:50Z","10000-01-01","1991"],"dc:description":["A transitive permutation representation of a finite group G is said to be multiplicity-free if each irreducible constituent of the associated permutation character of G occurs with multiplicity one. If H is a subgroup of G, then G acts naturally on the set of cosets of H. This action is transitive and the associated permutation character is given by the character 1$\\rm \\sbsp{H}{G}$ of G induced from the trivial character of H. If 1$\\rm \\sbsp{H}{G}$ is multiplicity-free, then H is said to be a multiplicity-free subgroup of G.","In this paper the multiplicity-free subgroups H of the alternating groups A$\\sb{\\rm n}$, n $>$ 18, are investigated and classified in the main chapter. The key tools involve bounds on the order of H and the analysis of the orbits of H on k-element subsets of the set of n elements on which A$\\sb{\\rm n}$ acts, k $\\leq$ n. The multiplicity-free subgroups of A$\\sb{\\rm n}$ are shown to have large orders and to be highly transitive. Explicit decompositions of several permutation characters are obtained.","A survey of the known results on multiplicity-free permutation representations is included. It is shown that 1$\\rm \\sbsp{H}{G}$ is multiplicity-free if and only if the algebra of complex-valued functions on G which are constant on the (H,H)-double cosets under the convolution product is commutative. The author proves that if G is a group of odd order which admits an involutary automorphism, and H is the subgroup of fixed points, then 1$\\rm \\sbsp{H}{G}$ is multiplicity-free.","Made available in DSpace on 2011-05-07T13:52:50Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9136537.pdf: 2745354 bytes, checksum: 428ac582bf9ed9205e06bd42ec3e23aa (MD5) Previous issue date: 1991","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:00:17Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:28:30-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9136537","(UMI)AAI9136537","http://hdl.handle.net/2142/22828"],"dc:language":["eng"],"dc:rights":["Copyright 1991 Balmaceda, Jose Maria P."],"dc:subject":["Mathematics"],"dc:title":["Multiplicity-free permutation representations of the alternating groups"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:20Z"}