θ-semisimple twisted conjugacy classes of type D in PSLn(q)

CARNOVALE, GIOVANNA; GARCÍA IGLESIAS, AGUSTÍN

JOURNAL OF LIE THEORY

HELDERMANN VERLAG

Lugar: Lemgo; Año: 2016 vol. 26

0949-5932

Let p be an odd prime, m∈ℕ and set q=pm,G=PSLn(q). Let θ be a standard graph automorphism ofG, d be a diagonal automorphism and Frq be the Frobeniusendomorphism of PSLn(𝔽q⎯⎯⎯⎯). We show thatevery (d∘θ)-conjugacy class of a (d∘θ,p)-regularelement in G is represented in some Frq-stable maximaltorus and that most of them are of type D. We write out the possible exceptionsand show that, in particular, if n≥5 is either odd or a multiple of 4and q>7, then all such classes are of type D. We develop general arguments todeal with twisted classes in finite groups.