Abstract
We deal with automorphisms of Sylow p-subgroups SΦ(Zp m) of Chevalley groups of normal types Φ, defined over residue rings Zp m of integers modulo p m, where m≥2 and >3 is a prime. It is shown that in this case all automorphisms of SΦ“Zp m” factor into a product of inner, diagonal, graph, central automorphisms and some explicitly specified automorphism of order p. The results obtained give the answer (under the condition that p>3) to Question 12.42 posed by Levchyuk in [4], which called for furnishing a description of automorphisms of a Sylow p-subgroup of a normal type Chevalley group over a residue ring of integers modulo pm, where m≥2 and p is a prime.
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Kolesnikov, S.G. Automorphisms of Sylow p-Subgroups of Chevalley Groups Defined over Residue Rings of Integers. Algebra and Logic 43, 17–33 (2004). https://doi.org/10.1023/B:ALLO.0000015128.63471.74
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DOI: https://doi.org/10.1023/B:ALLO.0000015128.63471.74