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On the nilpotency class of a multiplicative group of a modular group algebra of a dihedral 2-group

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Abstract

It is proved that the wreath product of a second-order group and the commutant of a dihedral group is imbedded into a multiplicative group of a modular group algebra of a dihedral group of order 2n. This implies that the nilpotency class of the multiplicative group is equal to 2n−2, i.e., to the order of the commutant of the dihedral group.

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References

  1. A. Shalev, On some conjectures concerning units inp-group algebras. Proceedings of the Second International Group Theory Conference (Bressanone, 1989),”Rend. Circ. Mat. Palermo, No. 23, 279–288 (1990).

    Google Scholar 

  2. J. T. Buckley, “Polynomial functions and wreath products”Ill. J. Math., No. 14, 274–282 (1970).

    Google Scholar 

  3. A. Shalev, “The nilpotency class of the unit group of a modular group algebra. I,”Isr. J. Math.,70, No. 3, 257–266 (1990).

    Google Scholar 

  4. A. Shalev, “Dimension subgroups, nilpotency indices, and the number of generators of ideals inp-group algebras,”J. Algebra, No. 129, 412–438 (1990).

    Google Scholar 

  5. R. K. Sharma and V. Bist, “A note on Lie nilpotent group rings,”Bull. Austral. Math. Soc.,45, No. 3, 503–506 (1992).

    Google Scholar 

  6. A. Sandling, “Presentations for the unit group of modular group algebras of groups of order 16,”Math. Comp.,59, No. 200, 689–701 (1992).

    Google Scholar 

  7. A. Shalev, “Lie dimension subgroups, Lie nilpotency indices, and the exponent of the group of normalized units,”J. London Math. Soc.,2, No. 43, 23–36 (1991).

    Google Scholar 

  8. A. K. Bhandari and I. B. S. Passi, “Lie nilpotency indices of group algebras,”Bull. London. Math. Soc.,24, No. 1, 68–70 (1992).

    Google Scholar 

  9. A. Shalev, “The nilpotency class of the unit group of a modular group algebra, III,”Arch. Math. (Basel), No. 60, 136–145 (1993).

    Google Scholar 

  10. X. Du, “The centers of radical rings,”Can. Math. Bull., No. 35, 174–179 (1992).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. B. Konovalov

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  1. A. B. Konovalov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 39–45, January, 1995.

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Konovalov, A.B. On the nilpotency class of a multiplicative group of a modular group algebra of a dihedral 2-group. Ukr Math J 47, 42–49 (1995). https://doi.org/10.1007/BF01058794

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  • DOI: https://doi.org/10.1007/BF01058794

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