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

Lucyna Szczepanik

Published: 1985-09-30

Vol. 1 (1985)

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

Lucyna Szczepanik

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 S^t from the schemes of fields C, R, F₃, F₅, Q₂(√-1), Q₂(√-2) and radical schemes S_i^β. We give a complete list of schemes for |g| ≤ 16, [g : R] ≤ 16 with all invariants.

Download files

PDF

Citation rules

Szczepanik, L. (1985). Fields and quadratic form schemes with the index of radical not exceeding 16. Annales Mathematicae Silesianae, 1, 23–46. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14334

References

1. C.M. Cordes, The Witt group and the equivalence of fields with respect to quadratic forms, J. Algebra 26 (1973), 400-421.
2. C.M. Cordes, Quadratic forms over non-formally real fields with a finite number of quaternion algebras, Pacific J. Math. 63 (1976), 357-365.
3. C.M. Cordes, Quadratic forms over fields with u = q/2 < ∞, Fund. Math. 99 (1978), 1-10.
4. C.M. Cordes, J. Ramsey, Quadratic forms over quadratic extensions of fields with two quaternion algebras, Canad. J. Math. 31 (1979), 1047-1058.
5. M. Kula, Fields with prescribed quadratic form schemes, Math. Z. 167 (1979), 201-212.
6. M. Kula, Fields and quadratic form schemes, this issue.
7. M. Kula, L. Szczepanik, K. Szymiczek, Quadratic forms over formally real fields with eight square classes, Manuscripta Math. 29 (1979), 295-303.
8. T.Y. Lam, The algebraic theory of quadratic forms, Reading 1973, Benjamin.
9. L. Szczepanik, Quadratic form schemes with non-trivial radical, Colloq. Math.
10. K. Szymiczek, A structure theorem for Grothendieck group of quadratic forms over a field, [w:] Colloquia Math. Soc. János Bolyai, Vol. 13, Topics in Number Theory, Debrecen, (1974), 389-397.
11. K. Szymiczek, Quadratic forms over fields with finite class number, Acta Arith. 28 (1975), 195-221. Google Scholar

Vol. 1 (1985)
Published: 1985-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

Submit