Some Galois extensions of quadratic extensions associated with Witt rings

Wenfeng Gao and Ján Miná\v{c}

A Galois field extension $E/F$ whose Galois group is a pro-$2$-group of an exponent of at most $8$, with a nilpotency class of at most $4$, is determined, such that it contains essential information about the Witt rings of all quadratic extensions of $F$.