Kronecker-weber plus Epsilon

We say that a group is almost abelian if every commutator is central and squares to the identity. Now let G be the Galois group of the algebraic closure of the field Q of rational numbers in the field C of complex numbers. Let Gab+ be the quotient of G universal for continuous homomorphisms to almost abelian profinite groups, and let Qab+ /Q be the corresponding Galois extension. We prove that Qab+ is generated by the roots of unity, the fourth roots of the rational primes, and the square roots of certain algebraic sine-monomials. The inspiration for the paper came from recent studies of algebraic 0-monomials by P. Das and by S. Seo.