An induction theorem for the unit groups of Burnside rings of 2-groups
| dc.citation.epage | 127 | en_US |
| dc.citation.epage | ||
| dc.citation.issueNumber | 1 | en_US |
| dc.citation.spage | 105 | en_US |
| dc.citation.volumeNumber | 289 | en_US |
| dc.contributor.author | Yalçin, E. | en_US |
| dc.date.accessioned | 2016-02-08T10:23:03Z | |
| dc.date.available | 2016-02-08T10:23:03Z | |
| dc.date.issued | 2005 | en_US |
| dc.department | Department of Mathematics | en_US |
| dc.description.abstract | Let G be a 2-group and B(G)× denote the group of units of the Burnside ring of G. For each subquotient H/K of G, there is a generalized induction map from B(H/K)× to B(G)× defined as the composition of inflation and multiplicative induction maps. We prove that the product of generalized induction maps ∏ B(H/K)× → B(G)× is surjective when the product is taken over the set of all subquotients that are isomorphic to the trivial group or a dihedral 2-group of order 2n with n ≥ 4. As an application, we give an algebraic proof for a theorem by Tornehave [The unit group for the Burnside ring of a 2-group, Aarhus Universitet Preprint series 1983/84 41, May 1984] which states that tom Dieck's exponential map from the real representation ring of G to B(G)× is surjective. We also give a sufficient condition for the surjectivity of the exponential map from the Burnside ring of G to B(G)×. © 2005 Elsevier Inc. All rights reserved. | en_US |
| dc.identifier.doi | 10.1016/j.jalgebra.2005.03.029 | en_US |
| dc.identifier.eissn | 1090-266X | |
| dc.identifier.issn | 0021-8693 | |
| dc.identifier.uri | http://hdl.handle.net/11693/24029 | |
| dc.language.iso | English | en_US |
| dc.publisher | Academic Press | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1016/j.jalgebra.2005.03.029 | en_US |
| dc.source.title | Journal of Algebra | en_US |
| dc.subject | Real representation ring | en_US |
| dc.subject | Units of Burnside ring | en_US |
| dc.title | An induction theorem for the unit groups of Burnside rings of 2-groups | en_US |
| dc.type | Article | en_US |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- An_induction_theorem_for_the_unit_groups_of_Burnside_rings_of_2_groups.pdf
- Size:
- 187.97 KB
- Format:
- Adobe Portable Document Format
- Description:
- Full printable version