ℚ-adequacy of Galois 2-extensions

The ℚ-adequacy of any finite Galois 2-extension of ℚ is shown to depend only on the ℚ-adequacy of its maximal elementary abelian intermediate field, which must be either quadratic (and hence always ℚ-adequate) or biquadratic over ℚ. A precise description of those biquadratic extensions of ℚ which are ℚ-adequate is given. This then gives a method for explicitly determining whether any given finite Galois 2-extension of ℚ can arise as a subfield of a ℚ-central division algebra.