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http://dx.doi.org/10.7858/eamj.2017.005

IRREDUCIBLE REPRESENTATIONS OF SOME METACYCLIC GROUPS WITH AN APPLICATION  

Sim, Hyo-Seob (Department of Applied Mathematics, Pukyong National University)
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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
metacyclic groups; irreducible representations; group algebras; right ideals;
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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.   DOI
7 H.S. Sim, Faithful irreducible representations of metacyclic groups, J. of Algebra, 170(3) (1994), 907-915.   DOI
8 Michio Suzuki, Group Theory I, Springer-Verlag (1982).