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    Self-dual modules in characteristic two and normal subgroups

    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

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    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,
    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:
    Depositing User: Dr. John Murray
    Date Deposited: 14 Dec 2023 13:50
    Journal or Publication Title: Journal of Algebra
    Publisher: Elsevier
    Refereed: Yes
    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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