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    Quadratic principal indecomposable modules and strongly real elements of finite groups


    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: https://doi.org/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
    URI:

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