Maximal abelian normal subgroups of Galois pro-2-groups
Let \(K\) be a field, \(\text{char} \neq 2\). Abelian normal subgroups of the pro-2-group \(\text{Gal} (K(2)/K)\), where \(K(2)\) is the quadratic closure of \(K\), were objects of interest of many papers. Under various additional assumptions on the field \(K\), \textit{R. Ware} [Pac. J. Math. 76, 541-564 (1978; Zbl 0405.12019), Commun. Algebra 13, 1713-1736 (1985; Zbl 0569.10008), Rocky Mt. J. Math. 19, 985-995 (1989; Zbl 0706.11023)] managed to point out a relatively large abelian normal subgroup of \(\text{Gal} (K(2)/K)\) with fully described structure (or at least rank). In this paper the authors show that the group \(\text{Gal} (K(2)/K)\) always contains the largest abelian normal subgroup. The details on the structure of this subgroup are in a strict relation to Ware's results.
scientific article; zbMATH DE number 614242