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:	Publisher Organisation
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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