Let A be an n-by-n nonderogatory matrix all of whose eigenvalues lie on the unit circle, and let and be nonnegative integers with + = n. Let ′ and ′ be positive integers and ′ a nonnegative integer with ′ + ′ + ...

A longstanding problem in the representation theory of finite solvable groups, sometimes called the Taketa problem, is to find strong bounds for the derived length dl(G) in terms of the number |cd(G)| of irreducible character ...