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Sibirsk. Mat. Zh., 2004, Volume 45, Number 2, Pages 319–328 (Mi smj1071)  

This article is cited in 9 scientific papers (total in 9 papers)

The weights of irreducible $SL_3(q)$-modules in the defining characteristic

A. V. Zavarnitsin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: This is a final step in solving the problem of recognition of the simple groups $L_3(p^k)$ by element orders. It is proven that when $L_3(p^k)$ acts on an elementary abelian $p$-group, there always appears an element of new order. A model is proposed for constructing the absolutely irreducible $p$-modular representations of $L_3(p^k)$ in polynomial spaces.

Keywords: modular representation, weight, element order, recognition

Full text: PDF file (240 kB)
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English version:
Siberian Mathematical Journal, 2004, 45:2, 261–268

Bibliographic databases:

UDC: 512.542
Received: 27.08.2003

Citation: A. V. Zavarnitsin, “The weights of irreducible $SL_3(q)$-modules in the defining characteristic”, Sibirsk. Mat. Zh., 45:2 (2004), 319–328; Siberian Math. J., 45:2 (2004), 261–268

Citation in format AMSBIB
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\paper The weights of irreducible $SL_3(q)$-modules in the defining characteristic
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\pages 319--328
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\zmath{https://zbmath.org/?q=an:1079.20019}
\transl
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 2
\pages 261--268
\crossref{https://doi.org/10.1023/B:SIMJ.0000021282.92576.f8}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Zavarnitsin, “Recognition of Simple Groups $U_3(Q)$ by Element Orders”, Algebra and Logic, 45:2 (2006), 106–116  mathnet  crossref  mathscinet  zmath
    2. Zavarnitsine AV, Mazurov VD, “Element orders in coverings of finite simple linear and unitary groups and recognizability of L-n(2) by spectrum”, Doklady Mathematics, 74:1 (2006), 569–572  crossref  mathscinet  zmath  isi  elib  scopus
    3. A. V. Zavarnitsin, V. D. Mazurov, “On element orders in coverings of the simple groups $L_n(q)$ and $U_n(q)$”, Proc. Steklov Inst. Math. (Suppl.), 257, suppl. 1 (2007), S145–S154  mathnet  crossref  mathscinet  elib
    4. V. D. Mazurov, G. Y. Chen, “Recognizability of finite simple groups $L_4(2^m)$ and $U_4(2^m)$ by spectrum”, Algebra and Logic, 47:1 (2008), 49–55  mathnet  crossref  mathscinet  zmath  isi
    5. A. V. Zavarnitsine, “Properties of element orders in covers for $\operatorname L_n(q)$ and $\operatorname U_n(q)$”, Siberian Math. J., 49:2 (2008), 246–256  mathnet  crossref  mathscinet  zmath  isi
    6. Zavarnitsine A.V., “On recognition by spectrum among covers of finite simple unitary and linear groups”, Doklady Mathematics, 78:1 (2008), 481–484  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. V. Vasil'ev, M. A. Grechkoseeva, A. M. Staroletov, “On finite groups isospectral to simple linear and unitary groups”, Siberian Math. J., 52:1 (2011), 30–40  mathnet  crossref  mathscinet  isi
    8. Grechkoseeva M.A., “Element Orders in Covers of Finite Simple Groups of Lie Type”, J. Algebra. Appl., 14:4 (2015), 1550056  crossref  mathscinet  zmath  isi  elib  scopus
    9. A. M. Staroletov, “O kompozitsionnykh faktorakh konechnykh grupp, izospektralnykh prostym klassicheskim gruppam”, Sib. matem. zhurn., 62:2 (2021), 422–440  mathnet  crossref
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