Geodesic
Invariant Theory of Abelian Transvection Groups
Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 404-411

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Let $G$ be a finite group acting linearly on the vector space $V$ over a field of arbitrary characteristic. The action is called coregular if the invariant ring is generated by algebraically independent homogeneous invariants, and the direct summand property holds if there is a surjective $k{{[V]}^{G}}$ -linear map $\pi \,:\,k[V]\,\to \,k{{[V]}^{G}}$ .The following Chevalley–Shephard–Todd type theorem is proved. Suppose $G$ is abelian. Then the action is coregular if and only if $G$ is generated by pseudo-reflections and the direct summand property holds.
DOI : 10.4153/CMB-2010-044-6
Mots-clés : 13A50 
Broer, Abraham. Invariant Theory of Abelian Transvection Groups. Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 404-411. doi: 10.4153/CMB-2010-044-6
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     title = {Invariant {Theory} of {Abelian} {Transvection} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {404--411},
     year = {2010},
     volume = {53},
     number = {3},
     doi = {10.4153/CMB-2010-044-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-044-6/}
}
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