Fields and quadratic form schemes with the index of radical not exceeding 16

Abstract

Let g be an elementary 2-group with — l e g and let d be a mapping of g into the family of all subgroups of g. The triple S = (g , — 1, d ) is called a quadratic form scheme if Q —C3 are fulfilled. The main result is: it )q\ ^ 16 or [fif: R] ^ 16 then all these schemes can be obtained as the product of schemes or schemes of form S‘ from the schemes of fields C, R, F3, Fs, Q2) Qt y /(—1), Qz (}/ —2) and radical schemes S^. We give a complete list of schemes for |£i| ^ 16, [gr: R] ^ 16 with all invariants.