  Given a homomorphism from a knot group to a fixed group, we introduce an
element of a $K_1$-group, which is a generalization of (twisted) Alexander
polynomials. We compare this $K_1$-class with other Alexander polynomials. In
terms of semi-local rings, we compute the $K_1$-classes of some knots and show
their non-triviality. We also introduce metabelian Alexander polynomials.
