One-class genera of exceptional groups over number fields
Journal de théorie des nombres de Bordeaux, Volume 30 (2018) no. 3, pp. 847-857.

We show that exceptional algebraic groups over number fields do not admit one-class genera of parahoric groups, except in the case G 2 . For the group G 2 , we enumerate all such one-class genera for the usual seven-dimensional representation.

Nous montrons que les groupes algébriques exceptionnels sur un corps de nombres n’admettent pas de genres de groupes parahoriques à une seule classe, sauf dans le cas de G 2 . Pour le groupe G 2 , nous énumérons tous les genres à une seule classe pour la représentation usuelle en dimension 7.

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DOI: 10.5802/jtnb.1052
Classification: 20G30, 20G41
Keywords: Class numbers, exceptional groups
Kirschmer, Markus 1

1 Lehrstuhl B für Mathematik RWTH Aachen University Pontdriesch 10–16 52062 Aachen, Germany
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Kirschmer, Markus. One-class genera of exceptional groups over number fields. Journal de théorie des nombres de Bordeaux, Volume 30 (2018) no. 3, pp. 847-857. doi : 10.5802/jtnb.1052. http://www.numdam.org/articles/10.5802/jtnb.1052/

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