Orbit decompositions of orthogonal monoids and the orders of finite orthogonal monoids

In this paper we determine the G × G orbits of both an even orthogonal monoid and an even special orthogonal monoid, where G is the unit group of the even special orthogonal monoid. We then use the orbit decompositions to compute the orders of these monoids over a finite field.

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Bibliographische Detailangaben
Veröffentlicht in:	Semigroup forum 2018-02, Vol.96 (1), p.105-125
Hauptverfasser:	Cao, You’an, Li, Zhenheng, Lei, Jie
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Decomposition Mathematics Mathematics and Statistics Monoids Research Article
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	In this paper we determine the G × G orbits of both an even orthogonal monoid and an even special orthogonal monoid, where G is the unit group of the even special orthogonal monoid. We then use the orbit decompositions to compute the orders of these monoids over a finite field.
ISSN:	0037-1912 1432-2137
DOI:	10.1007/s00233-017-9864-7