Suzuki-Ree groups and Tits mixed groups over rings

2018/08/17 by Andrei Smolensky, Smolensky, Andrei
Mathematics · #20D06 (Primary) 20G35 #20H25 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20D06 #msc:20G35 #msc:20H25

paper · pdf · doi:10.48550/arxiv.1808.05912

12 pages, 1 figure

arxiv created 2018/08/17 · arxiv updated 2018/08/20

Abstract

It is shown that Suzuki-Ree groups can be easily defined by means of comparing two fundamental representations of the ambient Chevalley group in characteristic 2 or 3. This eliminates the distinction between the Suzuki-Ree groups over perfect and imperfect fields and gives a natural definition for the analogues of such groups over commutative rings. As an application of the same idea, we explicitly construct a pair of polynomial maps between the groups of types B_n and C_n in characteristic 2 that compose to the Frobenius endomorphism. This, in turn, provides a simple definition for the Tits mixed groups over rings.

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