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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Defining normal subgroups of unipotent algebraic groups


Author: A. Fauntleroy
Journal: Proc. Amer. Math. Soc. 50 (1975), 14-19
MSC: Primary 20G15
DOI: https://doi.org/10.1090/S0002-9939-1975-0409674-8
MathSciNet review: 0409674
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Abstract: Let $ G$ be a connected unipotent algebraic group defined over the perfect field $ k$. We show that polynomial generators $ {x_1}, \cdots ,{x_n}$ for the ring $ k[G]$ can be chosen so that if $ N$ is any connected normal $ k$-closed subgroup of $ G$, then $ I(N)$ can be generated by $ \operatorname{co} \dim N$ $ p$-polynomials in $ {x_1}, \cdots ,{x_n}$ where $ p = \operatorname{char} k$. Moreover $ k[G/N]$ can also be generated as a polynomial algebra over $ k$ by $ p$-polynomials.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0409674-8
Keywords: Unipotent group, $ p$-polynomial, Frattini coordinates
Article copyright: © Copyright 1975 American Mathematical Society