Abstract
Let K be an infinite field of non-zero characteristic. Then, for any positive integer r, the general linear group GL r (K) has a natural action on the polynomial algebra K[x1,…,x r ] so that this algebra becomes a GL r (K)-module. The submodule structure of K[x1,…,x r ] was determined by S. R. Doty and L. Krop. The first part of this paper gives a full account of the main results of this theory. In the second part, the theory is applied to give a new proof of the result that if G is any finite subgroup of GL r (K) and K[x1,…,x r ] is regarded as a KG-module then K[x1,…,x r ] is asymptotically close to being a free KG-module.
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Bryant, R.M. (1995). Groups Acting on Polynomial Algebras. In: Hartley, B., Seitz, G.M., Borovik, A.V., Bryant, R.M. (eds) Finite and Locally Finite Groups. NATO ASI Series, vol 471. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0329-9_12
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DOI: https://doi.org/10.1007/978-94-011-0329-9_12
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