Geodesic
Serial group rings of classical groups defined over fields with odd number of elements
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 30, Tome 452 (2016), pp. 158-176 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We will make a list of simple finite classical groups defined over fields of odd characteristic, whose group rings over a given field are serial. 
@article{ZNSL_2016_452_a7,
     author = {A. V. Kukharev and G. E. Puninski},
     title = {Serial group rings of classical groups defined over fields with odd number of elements},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {158--176},
     year = {2016},
     volume = {452},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a7/}
}
TY  - JOUR
AU  - A. V. Kukharev
AU  - G. E. Puninski
TI  - Serial group rings of classical groups defined over fields with odd number of elements
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 158
EP  - 176
VL  - 452
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a7/
LA  - ru
ID  - ZNSL_2016_452_a7
ER  - 
%0 Journal Article
%A A. V. Kukharev
%A G. E. Puninski
%T Serial group rings of classical groups defined over fields with odd number of elements
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 158-176
%V 452
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a7/
%G ru
%F ZNSL_2016_452_a7
A. V. Kukharev; G. E. Puninski. Serial group rings of classical groups defined over fields with odd number of elements. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 30, Tome 452 (2016), pp. 158-176. http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a7/

[1] Yu. V. Volkov, A. V. Kukharev, G. E. Puninskii, “Polutsepnost gruppovogo koltsa konechnoi gruppy zavisit tolko ot kharakteristiki polya”, Zap. nauchn. semin. POMI, 423, 2014, 57–66

[2] A. V. Kukharev, G. E. Puninskii, “Polutsepnye gruppovye koltsa konechnykh grupp. $p$-nilpotentnost”, Zap. nauchn. semin. POMI, 413, 2013, 134–152 | MR

[3] A. V. Kukharev, G. E. Puninskii, “Polutsepnost gruppovykh kolets znakoperemennykh i simmetricheskikh grupp”, Vestnik BGU, ser. matem.-inform., 2014, no. 2, 61–64

[4] A. V. Kukharev, G. E. Puninskii, “Polutsepnye gruppovye koltsa konechnykh grupp. Sporadicheskie prostye gruppy i gruppy Sudzuki”, Zap. nauchn. semin. POMI, 435, 2015, 73–94

[5] A. V. Kukharev, G. E. Puninskii, “Polutsepnye gruppovye koltsa prostykh konechnykh grupp lieva tipa”, Fundam. prikl. matem. (to appear)

[6] R. W. Carter, Finite Groups of Lie Type: Conjugacy Classes and Complex Characters, John Wiley and Sons, 1985 | MR | Zbl

[7] D. Eisenbud, P. Griffith, “Serial rings”, J. Algebra, 17 (1971), 389–400 | DOI | MR | Zbl

[8] W. Feit, The Representation Theory of Finite Groups, North-Holland Mathematical Library, 25, 1982 | MR | Zbl

[9] W. Feit, “Possible Brauer trees”, Illinois J. Math., 28 (1984), 43–56 | MR | Zbl

[10] P. Fong, B. Srinivasan, “Brauer trees in classical groups”, J. Algebra, 131 (1990), 179–225 | DOI | MR | Zbl

[11] M. Geck, “Irreducible Brauer characters of the 3-dimensional unitary group in non-defining characteristic”, Comm. Algebra, 18:2 (1990), 563–584 | DOI | MR | Zbl

[12] D. G. Higman, “Indecomposable representations at characteristic $p$”, Duke Math. J., 21 (1954), 377–381 | DOI | MR | Zbl

[13] G. Hiss, G. Malle, “Low-dimensional representations of special unitary groups”, J. Algebra, 236 (2001), 745–767 | DOI | MR | Zbl

[14] P. Kleidman, M. Liebeck, The Subgroup Structure of the Finite Classical Groups, London Math. Soc. Lect. Note Series, 129, 1990 | MR | Zbl

[15] A. Kukharev, G. Puninski, “Serial group rings of finite groups. General linear and close groups”, Algebra Discrete Math., 20:1 (2015), 115–125 | MR | Zbl

[16] M. Livesey, On Rouquier blocks for finite classical groups at linear primes, arXiv: 1210.2225v1 | MR

[17] K. Morita, “On group rings over a modular field which possess radicals expressible as principal ideals”, Sci. Repts. Tokyo Daigaku, 4 (1951), 177–194 | MR | Zbl

[18] M. Sawabe, A. Watanabe, “On the principal blocks of finite groups with abelian Sylow $p$-subgroups”, J. Algebra, 237 (2001), 719–734 | DOI | MR | Zbl

[19] M. Stather, “Constructive Sylow theorems for the classical groups”, J. Algebra, 316 (2007), 536–559 | DOI | MR | Zbl

[20] A. J. Weir, “Sylow $p$-subgroups of the classical groups over finite fileds of characteristic prime to $p$”, Proc. Amer. Math. Soc., 6 (1955), 529–533 | MR | Zbl

[21] R. A. Wilson, The Finite Simple Groups, Graduate Texts in Mathematics, 251, Springer, 2009 | DOI | MR | Zbl