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Mat. Zametki, 1969, Volume 6, Issue 2, Pages 181–185 (Mi mz6921)  

A symplectic space with $p$-groups of operators over a field of characteristic $p$

Z. I. Borevich

Leningrad State University named after A. A. Zhdanov

Abstract: 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.

Full text: PDF file (380 kB)

English version:
Mathematical Notes, 1969, 6:2, 567–569

Bibliographic databases:

UDC: 512.4
Received: 13.12.1968

Citation: Z. I. Borevich, “A symplectic space with $p$-groups of operators over a field of characteristic $p$”, Mat. Zametki, 6:2 (1969), 181–185; Math. Notes, 6:2 (1969), 567–569

Citation in format AMSBIB
\Bibitem{Bor69}
\by Z.~I.~Borevich
\paper A~symplectic space with $p$-groups of operators over a~field of characteristic~$p$
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 2
\pages 181--185
\mathnet{http://mi.mathnet.ru/mz6921}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=252421}
\zmath{https://zbmath.org/?q=an:0195.33803|0188.11201}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 2
\pages 567--569
\crossref{https://doi.org/10.1007/BF01093699}


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