Gow, Rod and Murray, John
(2021)
Self-dual modules in characteristic two and normal subgroups.
Journal of Algebra, 570.
pp. 119-139.
ISSN 0021-8693
Abstract
We prove Clifford theoretic results which only hold in
characteristic 2. Let G be a finite group, let N be a normal subgroup of G and let ϕ be an irreducible 2-Brauer character of N. We show that ϕ occurs with odd multiplicity in the restriction of some self-dual irreducible Brauer character θ of G if and only if ϕ is G-conjugate to its dual. Moreover, if ϕ is self-dual then θ is unique and the multiplicity is 1. Next suppose that θ is a self-dual irreducible 2-Brauer
character of G which is not of quadratic type. We prove
that the restriction of θ to N is a sum of distinct self-dual irreducible Brauer character of N, none of which have
quadratic type. Moreover, G has no self-dual irreducible 2-
Brauer character of non-quadratic type if and only if N and
G/N satisfy the same property. Finally, suppose that b is a real 2-block of N. We show that there is a unique real 2-block of G covering b which is weakly regular with respect to N.
| Item Type: |
Article
|
| Additional Information: |
Cite as: Rod Gow, John Murray,
Self-dual modules in characteristic two and normal subgroups,
Journal of Algebra,
Volume 570,
2021,
Pages 119-139,
ISSN 0021-8693,
https://doi.org/10.1016/j.jalgebra.2020.11.014. |
| Keywords: |
Finite groups;
Representation theory;
Brauer characters;
Clifford theory;
Duality;
Quadratic modules;
Brauer blocks; |
| Academic Unit: |
Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: |
17955 |
| Identification Number: |
https://doi.org/10.1016/j.jalgebra.2020.11.014 |
| Depositing User: |
Dr. John Murray
|
| Date Deposited: |
14 Dec 2023 13:50 |
| Journal or Publication Title: |
Journal of Algebra |
| Publisher: |
Elsevier |
| Refereed: |
Yes |
| URI: |
|
| 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 |
Repository Staff Only(login required)
 |
Item control page |
Downloads per month over past year
Origin of downloads
Altmetric
Altmetric