East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

IRREDUCIBLE REPRESENTATIONS OF SOME METACYCLIC GROUPS WITH AN APPLICATION

  • Sim, Hyo-Seob (Department of Applied Mathematics, Pukyong National University)
  • Received : 2016.12.19
  • Accepted : 2016.12.23
  • Published : 2017.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

Motivated by the problem of determining all right ideals of a group algebra FG for a finite group G over a finite field F, we explicitly determine the faithful irreducible representations of some finite metacylic groups over finite fields. By using that result, we determine the structure of all right ideals of the group algebra for the symmetric group $S_3$ over a finite field F, as an example.

Keywords

References

  1. M. Barlotti, Faithful irreducible modules for the non-abelian groups of order pq, Lecture Note in Math., 1281 (1987), 1-8, Springer-Verlag.
  2. K. Doerk and T. Hawkes, Finite Soluble Group, Walter de Gruyter (1992).
  3. B. Huppert and N. Blackburn, Finite Groups II, Springer-Verlag (1982).
  4. R. Remak, Uber die Dastellung der endliechen Gruppen als Untergruppen direkter Produkte, J. Reine Angew. Math., 163 (1930), 1-44.
  5. R. Schmidt, Subgroup Lattices of Groups, Walter de Gruyter (1994).
  6. H.S. Sim, Degree of irreducible representations of metacyclic groups, Comm. in Algebra, 21(10) (1993), 3773-3777. https://doi.org/10.1080/00927879308824764
  7. H.S. Sim, Faithful irreducible representations of metacyclic groups, J. of Algebra, 170(3) (1994), 907-915. https://doi.org/10.1006/jabr.1994.1369
  8. Michio Suzuki, Group Theory I, Springer-Verlag (1982).