Dade groups for finite groups and dimension functions

buir.contributor.authorGelvin, Matthew
buir.contributor.authorYalçın, Ergün
buir.contributor.orcidGelvin, Matthew|0000-0001-6529-4116
buir.contributor.orcidYalçın, Ergün|0000-0001-8799-5490
dc.citation.epage196en_US
dc.citation.spage146en_US
dc.citation.volumeNumber576en_US
dc.contributor.authorGelvin, Matthew
dc.contributor.authorYalçın, Ergün
dc.date.accessioned2022-02-18T08:34:31Z
dc.date.available2022-02-18T08:34:31Z
dc.date.issued2021-06-15
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractLet G be a finite group and k an algebraically closed field of characteristic p > 0. We define the notion of a Dade kG-module as a generalization of endo-permutation modules for p-groups. We show that under a suitable equivalence relation, the set of equivalence classes of Dade kG-modules forms a group under tensor product, and the group obtained this way is isomorphic to the Dade group D(G) defined by Lassueur. We also consider the subgroup DΩ(G) of D(G) generated by relative syzygies ΩX , where X is a finite G-set. If C(G, p) denotes the group of superclass functions defined on the p-subgroups of G, there are natural generators ωX of C(G, p), and we prove the existence of a well-defined group homomorphism ΨG : C(G, p) → DΩ(G) that sends ωX to ΩX . The main theorem of the paper is the verification that the subgroup of C(G, p) consisting of the dimension functions of k-orientable real representations of G lies in the kernel of ΨG.en_US
dc.description.provenanceSubmitted by Samet Emre (samet.emre@bilkent.edu.tr) on 2022-02-18T08:34:31Z No. of bitstreams: 1 Dade_groups_for_finite_groups_and_dimension_functions.pdf: 775501 bytes, checksum: 64bc5c7777ae88af096297a8cc6c5b8c (MD5)en
dc.description.provenanceMade available in DSpace on 2022-02-18T08:34:31Z (GMT). No. of bitstreams: 1 Dade_groups_for_finite_groups_and_dimension_functions.pdf: 775501 bytes, checksum: 64bc5c7777ae88af096297a8cc6c5b8c (MD5) Previous issue date: 2021-06-15en
dc.embargo.release2023-06-15
dc.identifier.doi10.1016/j.jalgebra.2021.01.035en_US
dc.identifier.issn0021-8693
dc.identifier.urihttp://hdl.handle.net/11693/77495
dc.language.isoEnglishen_US
dc.publisherAcademic Pressen_US
dc.relation.isversionofhttps://doi.org/10.1016/j.jalgebra.2021.01.035en_US
dc.source.titleJournal of Algebraen_US
dc.subjectDade groupen_US
dc.subjectEndo-permutation moduleen_US
dc.subjectBurnside ringen_US
dc.subjectBorel-Smith functionsen_US
dc.titleDade groups for finite groups and dimension functionsen_US
dc.typeArticleen_US

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