On the characters and commutators of finite algebra groups. (Q1883023)

A finite algebra group is a group of the form \(1+J(A)\), where \(A\) is a finite dimensional algebra over a finite field, and \(J(A)\) is the Jacobson radical of \(A\). Subgroups of the form \(1+U\), where \(U\) is a subalgebra of \(J(A)\) are called algebra subgroups. The author proves that every irreducible character of an algebra group is induced from a linear character of an algebra subgroup. This result answers a question of I.~M.~Isaacs, and it is achieved by establishing a new commutator identity which holds in algebra groups.