Abstract
We give an elementary proof of the following result. Let C be an abelian and irreducible subgroup of the symplectic group Sp(2m, p). Then C is cyclic and embeds in the (multiplicative) subgroup of order \(p^m + 1\) of the field of order \(p^{2m}\). The proof yields, in fact, a similar result for nonsingular bilinear forms more generally.
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Turull, A. Abelian groups acting irreducibly and bilinear forms. Arch. Math. 121, 351–354 (2023). https://doi.org/10.1007/s00013-023-01918-2
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DOI: https://doi.org/10.1007/s00013-023-01918-2