Geodesic
Serial group rings of finite groups. Sporadic simple groups and Suzuki groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 28, Tome 435 (2015), pp. 73-94 
A. V. Kukharev; G. E. Puninski. Serial group rings of finite groups. Sporadic simple groups and Suzuki groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 28, Tome 435 (2015), pp. 73-94. http://geodesic.mathdoc.fr/item/ZNSL_2015_435_a4/
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     author = {A. V. Kukharev and G. E. Puninski},
     title = {Serial group rings of finite groups. {Sporadic} simple groups and {Suzuki} groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_435_a4/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

For each prime $p$ we make a list of simple sporadic finite groups and Suzuki groups whose $p$-modular group ring is serial.

[1] F. W. Anderson, K. R. Fuller, Rings and categories of modules, Springer Graduate Texts in Math., 13, 2nd edition, 1992 | DOI | MR | Zbl

[2] D. J. Benson, Representations and Cohomology, v. I, Cambridge University Press, 1995

[3] H. I. Blau, “On Brauer stars”, J. Algebra, 90 (1984), 169–188 | DOI | MR | Zbl

[4] W. Bosma, J. Cannon, C. Playoust, “The Magma algebra system. I: The user language”, J. Symb. Comp., 24:3/4 (1997), 235–265 http://magma.maths.usyd.edu.au/magma/ | DOI | MR | Zbl

[5] T. Breuer et al., The modular atlas homepage: decomposition matrices, http://magma.maths.usyd.edu.au/magma/

[6] R. Burkhardt, “Die Zerlegungsmatrizen der Gruppen $\mathrm{PSL}(2,p^f)$”, J. Algebra, 40 (1976), 75–96 | DOI | MR | Zbl

[7] R. Burkhardt, “Über die Zerlegungszahlen der Suzukigruppen $\mathrm{Sz}(q)$”, J. Algebra, 59 (1979), 421–433 | DOI | MR | Zbl

[8] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of finite groups: maximal subgroups and ordinary characters for simple groups, Clarendon Press, Oxford, 1985 | MR | Zbl

[9] G. Cooperman, G. Hiss, K. Lux, J. Müller, “The brauer tree of the principal 19-block of the sporadic simple Thompson group”, Exp. Math., 6:4 (1997), 293–300 | DOI | MR | Zbl

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

[11] The GAP Group, Groups, Algorithms, and Programming, Version 4.6.5, 2013, http://www.gap-system.org/

[12] L. Héthely, E. Horváth, F. Petényi, The depth of subgroups of Suzuki groups, arXiv: 1404.1523v1 | MR

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

[14] G. Hiss, K. Lux, Brauer trees of sporadic groups, Clarendon Press, 1989 | MR | Zbl

[15] G. Hiss, K. Lux, “The Brauer characters of the Hall–Janko group”, Comm. Algebra, 16:2 (1988), 357–398 | DOI | MR | Zbl

[16] G. Hiss, C. Jansen, K. Lux, R. Parker, Computational modular character theory, Preprint, 1993

[17] A. Kukharev, G. Puninski, “Serial group rings of finite groups. $p$-solvability”, Algebra Discrete Math., 16:2 (2013), 201–216 | MR | Zbl

[18] A. Khosravi, B. Khosravi, “Two new characterizations for sporadic simple groups”, Pure math. and appl., 16:3 (2005), 287–293 | MR | Zbl

[19] J. Müller, M. Neunhöffer, F. Röhr, R. Wilson, “Completing the Brauer trees for the sporadic simple Lyons group”, LMS J. Comput. Math., 5 (2002), 18–33 | DOI | MR | Zbl

[20] R. P. Martineau, “On representations of the Suzuki groups over fields of odd characteristic”, J. London Math. Soc., 6 (1972), 153–160 | DOI | MR | Zbl

[21] V. S. Monakhov, A. A. Trofimuk, “Invarianty konechnykh razreshimykh grupp”, PFMT, 1:2 (2010), 63–81 | Zbl

[22] 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

[23] N. Naehrig, “A construction of almost all Brauer trees”, J. Group Theory, 11:6 (2008), 813–829 | DOI | MR | Zbl

[24] G. Puninski, Serial rings, Kluwer, 2001 | MR | Zbl

[25] B. Srinivasan, “On the indecomposable representations of a certain class of groups”, Proc. Lond. Math. Soc., 10 (1960), 497–513 | DOI | MR | Zbl

[26] M. Suzuki, “On a class of doubly transitive groups over fields of odd characteristic”, J. Lond. Math. Soc., 6 (1972), 153–160

[27] H. Wielandt, “Sylowgruppen und Kompositions-Struktur”, Abhand. Math. Sem. Hamburg, 22 (1958), 215–228 | DOI | MR | Zbl

[28] 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

[29] A. V. Kukharev, “Polutsepnost gruppovykh kolets unimodulyarnykh proektivnykh grupp”, Sbornik rabot 71-oi nauchnoi konferentsii studentov i aspirantov Belorus. gos. un-ta, Ch. 1, Izd. tsentr BGU, Minsk, 2014, 11–14

[30] A. V. Kukharev, G. E. Puninskii, “Polutsepnost gruppovykh kolets znakoperemennykh i simmetricheskikh grupp”, Vestnik BGU, ser. matematika, 2 (2014), 61–64

[31] U. Feit, Teoriya predstavlenii konechnykh grupp, Nauka, M., 1990 | MR