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Using the mixed Lie algebras of Lazard, we extend the results of the firstauthor on mild groups to the case p=2. In particular, we show that for anyfinite set S_0 of odd rational primes we can find a finite set S of oddrational primes containing S_0 such that the Galois group of the maximal2-extension of Q unramified outside S is mild. We thus produce a projectivesystem of such Galois groups which converge to the maximal pro-2-quotient ofthe absolute Galois group of $\Q$ unramified at 2 and $\infty$. Our resultsalso allow results of Alexander Schmidt on pro-p-fundamental groups of markedarithmetic curves to be extended to the case p=2 over a global field which iseither a function field of odd characteristic or a totally imaginary numberfield.

Mild pro-2-groups and 2-extensions of Q with restricted ramification