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Outer unipotent classes in automorphism groups of simple algebraic groups
Author(s) -
Lawther Ross,
Liebeck Martin W.,
Seitz Gary M.
Publication year - 2014
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdu011
Subject(s) - unipotent , mathematics , morphism , algebraic group , outer automorphism group , automorphism , pure mathematics , simple (philosophy) , algebraic number , coset , group of lie type , reductive group , combinatorics , automorphism group , group theory , mathematical analysis , philosophy , epistemology
We study the unipotent elements of disconnected algebraic groups of the form G 〈 τ 〉 , where G is a simple algebraic group in characteristic p possessing a graph automorphism τ of order p . We classify the unipotent classes in the coset G τ and determine the corresponding centralizers, showing that these bear a close relation to classes in a certain natural connected overgroup of G 〈 τ 〉 . We also obtain a formula for the total number of outer unipotent elements in the finite groupG γ 〈 τ 〉 , where γ is a Frobenius morphism, analogous to the well‐known Steinberg formula for the number of inner unipotent elements.