A~symplectic space with $p$-groups of operators over a~field of characteristic~$p$
Matematičeskie zametki, Tome 6 (1969) no. 2, pp. 181-185
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Let $K$ be a field of nonzero characteristic pne2, let $G$ be a finite $p$-group, and let $M$ be a nondegenerate finite-dimensional symplectic space over $K$ with the matching structure of a $G$-module. It is proven that if $M$ is a free $K[G]$-module then there exists in $M$ a normal basis with a canonical Gram matrix.
@article{MZM_1969_6_2_a5,
author = {Z. I. Borevich},
title = {A~symplectic space with $p$-groups of operators over a~field of characteristic~$p$},
journal = {Matemati\v{c}eskie zametki},
pages = {181--185},
publisher = {mathdoc},
volume = {6},
number = {2},
year = {1969},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_2_a5/}
}
Z. I. Borevich. A~symplectic space with $p$-groups of operators over a~field of characteristic~$p$. Matematičeskie zametki, Tome 6 (1969) no. 2, pp. 181-185. http://geodesic.mathdoc.fr/item/MZM_1969_6_2_a5/