Geodesic
Automorphisms of Sylow $p$-Subgroups of Chevalley Groups Defined over Residue Rings of Integers
Algebra i logika, Tome 43 (2004) no. 1, pp. 32-59 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We deal with automorphisms of Sylow $p$-subgroups $S\Phi(Z_{p^m})$ of Chevalley groups of normal types $\Phi$, defined over residue rings $Z_{p^m}$ of integers modulo $p^m$, where $m\geqslant 2$ and $p>3$ is a prime. It is shown that in this case all automorphisms of $S\Phi(Z_{p^m})$ 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 $p^m$, where $m\geqslant 2$ and $p$ is a prime.
Keywords: Chevalley group, Sylow $p$-subgroup
Mots-clés : automorphism. 
@article{AL_2004_43_1_a1,
     author = {S. G. Kolesnikov},
     title = {Automorphisms of {Sylow} $p${-Subgroups} of {Chevalley} {Groups} {Defined} over {Residue} {Rings} of {Integers}},
     journal = {Algebra i logika},
     pages = {32--59},
     year = {2004},
     volume = {43},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2004_43_1_a1/}
}
TY  - JOUR
AU  - S. G. Kolesnikov
TI  - Automorphisms of Sylow $p$-Subgroups of Chevalley Groups Defined over Residue Rings of Integers
JO  - Algebra i logika
PY  - 2004
SP  - 32
EP  - 59
VL  - 43
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AL_2004_43_1_a1/
LA  - ru
ID  - AL_2004_43_1_a1
ER  - 
%0 Journal Article
%A S. G. Kolesnikov
%T Automorphisms of Sylow $p$-Subgroups of Chevalley Groups Defined over Residue Rings of Integers
%J Algebra i logika
%D 2004
%P 32-59
%V 43
%N 1
%U http://geodesic.mathdoc.fr/item/AL_2004_43_1_a1/
%G ru
%F AL_2004_43_1_a1
S. G. Kolesnikov. Automorphisms of Sylow $p$-Subgroups of Chevalley Groups Defined over Residue Rings of Integers. Algebra i logika, Tome 43 (2004) no. 1, pp. 32-59. http://geodesic.mathdoc.fr/item/AL_2004_43_1_a1/

[1] J. A. Gibbs, “Automorphisms of certain unipotent groups”, J. Algebra, 14:2 (1970), 203–228 | DOI | MR | Zbl

[2] V. M. Levchuk, “Avtomorfizmy unipotentnykh podgrupp grupp lieva tipa malykh rangov”, Algebra i logika, 29:2 (1990), 141–161 | MR | Zbl

[3] V. M. Levchuk, “Avtomorfizmy unipotentnykh podgrupp grupp Shevalle”, Algebra i logika, 29:3 (1990), 315–338 | MR | Zbl

[4] Nereshennye voprosy teorii grupp. Kourovskaya tetrad, 15-e izd., In-t matem. SO RAN, Novosibirsk, 2002 | MR

[5] V. M. Levchuk, “Kommutatornoe stroenie nekotorykh podgrupp grupp Shevalle”, Ukr. matem. zh., 44:6 (1992), 786–795 | MR | Zbl

[6] N. Burbaki, Gruppy i algebry Li, Glavy IV–VI, Mir, M., 1972 | MR | Zbl

[7] R. Carter, Simple groups of Lie type, Wiley and Sons, New York, 1972 | MR | Zbl