Irreducible Characters of Finite Algebra Groups
Abstract
Description
Let F be a finite field with q elements, let A be a finite dimensional F-algebra and let J=J(A) be the Jacobson radical of A. Then G=1+J is a p-group, where p is the characteristic of F. We refer to G as an F-algebra group. A subgroup H of G is said to be an algebra subgroup of G if H=1+U for some multiplicatively closed F-subspace of J. In this paper, we parametrize the irreducible complex characters of G in terms of G-orbits on the dual space of J. Moreover, we prove that every irreducible complex character of G is induced from a linear character of some algebra subgroup of G.
19 pages, Latex2e (amsart), uses amssymb and amsfonts. Submitted to the Journal of Group Theory
19 pages, Latex2e (amsart), uses amssymb and amsfonts. Submitted to the Journal of Group Theory