Skip to main content
SpringerLink
Log in

On the indices of simple components of twisted group algebras of finite groups over a P-adic number field

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

It is shown that if 2≢0 (mod P) the set of indices of simple components of the twisted group algebra of finite nilpotent groups of class 2 over the field of P-adic numbers consists of all natural numbers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. R. Brauer, “Untersuchungen über die arithmetischen eigenschaften von gruppen linearer Substitutionen. II,” Math. Z.,31, 737–747 (1930).

    Google Scholar 

  2. P. Roquette, “Realisierung von darstellungen endlicher nilpotenter gruppen,” Arch. Math.,9, 241–250 (1958).

    Google Scholar 

  3. S. D. Berman, “On the Schur index,” Usp. Mat. Nauk,2, 95–99 (1961).

    Google Scholar 

  4. S. D. Berman, “Representations of finite groups over an arbitrary field and over rings of integers,” Izv. Akad. Nauk SSSR, Ser. Mat.,30, 69–132 (1966).

    Google Scholar 

  5. S. D. Berman, “On the Schur index of characters of finite groups with respect to a local field,” in: All-Union Colloquium on General Algebra, Riga (1967), p. 15.

  6. L. F. Barannik, “On the Schur index of protective representations of finite groups,” Mat. Sb.,86, No. 1, 110–120 (1971).

    Google Scholar 

  7. T. Yamada, The Schur Subgroup of the Brauer Group, Lecture Notes in Mathematics,397, 1–159 (1974).

    Google Scholar 

  8. V. F. Barannik, “On the Schur index of projective representations of finite groups with respect to a local field,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 10, 3–5 (1982).

    Google Scholar 

  9. A. Weil, Basic Number Theory, Springer-Verlag, Berlin, Heidelberg, New York (1974).

    Google Scholar 

  10. A. A. Albert, Structure of Algebras, Academic Press, New York (1939).

    Google Scholar 

  11. H. Hasse, Zahlentheorie, Akademie-Verlag, Berlin (1969).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Uzhgorod University, USSR

    V. F. Barannik & L. F. Barannik

  2. Poltava Pedagogical Institute, USSR

    V. F. Barannik & L. F. Barannik

Authors
  1. V. F. Barannik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. F. Barannik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 6, pp. 723–727, June, 1991.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barannik, V.F., Barannik, L.F. On the indices of simple components of twisted group algebras of finite groups over a P-adic number field. Ukr Math J 43, 673–676 (1991). https://doi.org/10.1007/BF01058933

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01058933

Keywords

Search

Navigation