Fields and quadratic form schemes with the index of radical not exceeding 16
Abstract
Let g be an elementary 2-group with -1∈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 C1-C3 are fulfilled. The main result is: if |g| ≤ 16 or [g : R] ≤ 16 then all these schemes can be obtained as the product of schemes or schemes of form St from the schemes of fields C, R, F3, F5, Q2(√-1), Q2(√-2) and radical schemes Siβ. We give a complete list of schemes for |g| ≤ 16, [g : R] ≤ 16 with all invariants.
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Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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