Unit groups of group algebras of groups of order 20

Abstract

Let F be a nite eld of characteristic p. There are ve non-isomorphic groups of order 20. The structure of U(FD₂₀) is given in [2, 6, 10] and  that of U(FQ₂₀₎ is given in [3, 6], for p = 2; 5. In this article, the unit groups of the group algebras FG are established for all the remaining groups of order 20, namely, U(FC₂₀), U(F(C₁₀xC₂)), U(FQ₂₀) (the semisimple case) and U(FGA(1; 5)) where GA(1; 5) is the general affine group of order 20 which is isomorphic to a semidirect product of C₅ and C₄.

Key words: Group algebras, dihedral groups, quaternion groups, general affine groups.