Unit groups of group algebras of groups of order 20
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.