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The Lengths of Group Algebras of Small-Order Groups

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The paper evaluates the lengths of group algebras of all groups of orders not exceeding 7 over an arbitrary field.

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References

  1. L. Babai and Á. Seress, “On the diameter of permutation groups,” Eur. J. Combin., 13, 231–243 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  2. E. B. Vinberg, A Course in Algebra [in Russian], 3rd ed., Factorial Press, Moscow (2002).

    Google Scholar 

  3. M. M. Glukhov and A. Yu. Zubov, “On lengths of symmetric and alternate permutation groups in different generating systems (a survey),” Math. Probl. Cybern., 8, 5–32 (1999).

    MATH  Google Scholar 

  4. A. E. Guterman, O. V. Markova, and M. A. Khrystik, “On the lengths of group algebras of finite Abelian groups in the semi-simple case,” Preprint (2018).

  5. A. E. Guterman, O. V. Markova, and M. A. Khrystik, “On the lengths of group algebras of finite Abelian groups in the modular case,” Preprint (2018).

  6. A. Guterman, T. Laffey, O. Markova, and H. Šmigoc, “A resolution of Paz’s conjecture in the presence of a nonderogatory matrix,” Linear Algebra Appl., 543, 234–250 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Guterman, O. Markova, and V. Mehrmann, “Length realizability for pairs of quasi-commuting matrices,” Linear Algebra Appl., DOI: https://doi.org/10.1016/j.laa.2018.06.020.

  8. O. V. Markova, “An upper bound for the length of commutative algebras,” Mat. Sb., 200, 41–62 (2009).

    Article  MathSciNet  Google Scholar 

  9. O. V. Markova, “The length function and matrix algebras,” Fundam. Prikl. Mat., 17, 65–173 (2012).

    Google Scholar 

  10. C. J. Pappacena, “An upper bound for the length of a finite-dimensional algebra,” J. Algebra, 197, 535–545 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  11. D. S. Passman, The Algebraic Structure of Group Rings, Wiley-Interscience, New York (1977).

    MATH  Google Scholar 

  12. A. Paz, “An application of the Cayley–Hamilton theorem to matrix polynomials in several variables,” Linear Multilinear Algebra, 15, 161–170 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  13. R. S. Pierce, Associative Algebras, Springer-Verlag, New York–Berlin (1982).

    Book  MATH  Google Scholar 

  14. R. K. Sharma, J. B. Srivastava, and M. Khan, “The unit group of 𝔽S 3,” Acta Math. Acad. Paedagog. Nyházi., 23, 129–142 (2007).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    A. E. Guterman & O. V. Markova

  2. Moscow Insitute of Physics and Technology, Moscow Region, Dolgoprudnii, Russia

    A. E. Guterman & O. V. Markova

Authors
  1. A. E. Guterman
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  2. O. V. Markova
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Corresponding author

Correspondence to A. E. Guterman.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 472, 2018, pp. 76–87.

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Guterman, A.E., Markova, O.V. The Lengths of Group Algebras of Small-Order Groups. J Math Sci 240, 754–761 (2019). https://doi.org/10.1007/s10958-019-04391-x

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  • DOI: https://doi.org/10.1007/s10958-019-04391-x

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