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Group of automorphisms of the ring ℤA4

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Abstract

The structure of the group of automorphisms of the integer group ring of the group A4 is studied in terms of a semidirect product. We show that the Zassenhaus conjecture on the structure of automorphisms of integer group rings of finite groups for the group Aut ℤA4 holds.

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References

  1. E. V. Grachev and A. M. Popova, “Units of integral group ring of the group A5,” Vestn. Krasnoyarsk. Gos. Univ. Fiz.-Mat. Nauki, No. 4, 54–59 (2006).

  2. E. V. Grachev and A. M. Popova, “Multiplicative group of the ring ℤA6,” in: Int. Conf. “Algebra and Its Applications.” Thesises of Reports, Krasnoyarsk (2007), pp. 38–39.

  3. R. S. Pierce, Associative Algebras, Grad. Texts Math., Springer (1982).

  4. A. M. Popova, “Group of automorphisms of the ring ℤS3,” Algebra Model Theory, 6, 84–91 (2007).

    Google Scholar 

  5. A. M. Popova, “Group of automorphisms of the ring ℤD12,” J. Sib. Federal Univ. Math. Phys., 1, No. 3, 323–328 (2008).

    Google Scholar 

  6. A. M. Popova and E. V. Grachev, “Group of units of integral group ring of the group S5,” in: Abelian Groups. Proc. All-Russian Symp., Biisk (2006).

  7. A. M. Popova and E. V. Grachev, “Group of automorphisms of the ring ℤS4,” in: Proc. Int. Sci. Conf. “Modern Problems of Mathematics, Computer Science, and Cybernetics,” Almaty (2008), pp. 469–470.

  8. A. M. Popova and E. N. Poroshenko, “Group of units in integral group rings of finite groups,” Algebra Model Theory, 4, 99–106 (2003).

    Google Scholar 

  9. A. M. Popova and S. V. Zhurkov, “Group of units of integer group ring of the group SL2(3),” Algebra Model Theory, 5, 170–181 (2005).

    MathSciNet  Google Scholar 

  10. A. M. Popova and S. V. Zhurkov, “Invertible elements of integral group rings,” in: Int. Algebraic Conf. Thesises of Reports, Ekaterinburg (2005), pp. 69–70.

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Authors and Affiliations

  1. Novosibirsk State Technical University, Novosibirsk, Russia

    A. M. Popova

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  1. A. M. Popova
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Correspondence to A. M. Popova.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 14, No. 5, pp. 185–189, 2008.

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Popova, A.M. Group of automorphisms of the ring ℤA4 . J Math Sci 163, 751–754 (2009). https://doi.org/10.1007/s10958-009-9712-8

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  • DOI: https://doi.org/10.1007/s10958-009-9712-8

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