Groups with large Noether bound  [ Les groupes pour lesquels la borne de Noether est grande ]
Annales de l'institut Fourier, Tome 64 (2014) no. 3 , p. 909-944
doi : 10.5802/aif.2868
URL stable : http://www.numdam.org/item?id=AIF_2014__64_3_909_0

Classification:  13A50,  11B50
Mots clés: La borne de Noether, invariants polynômiaux, suites de somme nulle
Nous classifions les groupes finis ayant un invariant polynômial indécomposable de degré au moins la moitié de l’ordre du groupe. Il est démontré qu’en exceptant quatre groupes particuliers, ce sont exactement les groupes avec un sous-groupe cyclique d’indice au plus deux.
The finite groups having an indecomposable polynomial invariant of degree at least half the order of the group are classified. It turns out that –apart from four sporadic exceptions– these are exactly the groups with a cyclic subgroup of index at most two.

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