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Gow, Roderick and Murray, John (2019) Quadratic principal indecomposable modules and strongly real elements of finite groups. Proceedings of the American Mathematical Society, 147. pp. 2783-2796. ISSN 1088-6826
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Abstract
Let P be a principal indecomposable module of a finite group G in characteristic 2 and let φ be the Brauer character of the corresponding simple G-module. We show that P affords a non-degenerate G-invariant quadratic form if and only if there are involutions s,t∈G such that st has odd order and φ(st)/2 is not an algebraic integer.
We then show that the number of isomorphism classes of quadratic principal indecomposable G-modules is equal to the number of strongly real conjugacy classes of odd order elements of G.
| Item Type: | Article |
|---|---|
| Additional Information: | This is the preprint version of the published article, which can be cited as: arXiv:1803.03182. T |
| Keywords: | Quadratic principal; indecomposable; modules; strongly real elements; finite Groups; |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 13520 |
| Identification Number: | 10.1090/proc/14441 |
| Depositing User: | Dr. John Murray |
| Date Deposited: | 11 Nov 2020 15:45 |
| Journal or Publication Title: | Proceedings of the American Mathematical Society |
| Publisher: | American Mathematical Society |
| Refereed: | Yes |
| Related URLs: | |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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