References
- Artin, E. (1950). Questions de base minimale dans la théorie des nombres algébriques. In: Algèbre et Théorie Des Nombres. Colloq. Internat. CNRS, Vol. 24. Paris: CNRS, pp. 19–20.
- Byott, N. P., Greither, C., Sodaïgui, B. (2006). Classes réalisables d’extensions non abéliennes. J. Reine Angew. Math. 2006(601):1–27. DOI: https://doi.org/10.1515/CRELLE.2006.093.
- Byott, N. P., Sodaïgui, B. (2013). Realizable Galois module classes over the group ring for non abelian extensions. Ann. Inst. Fourier (Grenoble). 63(1):303–371. DOI: https://doi.org/10.5802/aif.2762.
- Cohen, H. (2000). Advanced Topics in Computational Number Theory. Grad. Texts in Math., Vol. 193. New York: Springer-Verlag.
- Conner, P. E., Hurrelbrink, J. (1988). Class Number Parity. Series in Pure Math., Vol. 8. Singapore: World Scientific.
- Curtis, C. W., Reiner, I. (1987). Methods of Representation Theory with Applications to Finite Groups and Orders, Vol. II. New York: Wiley-Interscience.
- Fröhlich, A. (1960). The discriminant of relative extensions and the existence of integral bases. Mathematika. 7(1):15–22. DOI: https://doi.org/10.1112/S0025579300001534.
- Fröhlich, A. (1983). Galois Module Structure of Algebraic Integers. Berlin: Springer-Verlag.
- Fröhlich, A. (1985). Orthogonal representations of Galois groups, Stiefel-Whitney classes and Hass-Witt invariants. J. Reine Angew. Math. 360:84–123.
- Fröhlich, A., Taylor, M. J. (1991). Algebraic Number Theory. Cambridge: Cambridge University Press.
- Gordon, J., Martin, L. (2001). Representations and Characters of Groups, 2nd ed. New York: Cambridge University Press.
- Groupprops. Linear representation theory of groups of order 32. https://groupprops.subwiki.org/wiki/
- Grundman, H. G., Smith, T. L. (1996). Automatic realizability of Galois groups of order 16. Proc. Amer. Math. Soc. 124(9):2631–2640. DOI: https://doi.org/10.1090/S0002-9939-96-03345-X.
- Grundman, H. G., Smith, T. L., Swallow, J. R. (1995). Groups of order 16 as Galois groups. Expo. Math. 13:289–319.
- Hecke, E. (1981). Lectures on the Theory of Algebraic Numbers. Grad. Texts in Math., Vol. 77. New York: Springer-Verlag.
- Lam, T. Y. (1973). The Algebraic Theory of Quadratic Forms (Revised printing 1980). New York/Boston, MA: Benjamin/Addison-Wesley.
- Ledet, A. (1995). On 2-groups as Galois groups. Can. J. Math. 47(6):1253–1273. DOI: https://doi.org/10.4153/CJM-1995-064-3.
- McCulloh, L. R. (1987). Galois module structure of abelian extensions. J. Reine Angew. Math. 375(376):259–306.
- Neukirch, J. (1973). Über das Einbettungsproblem der algebraischen Zahlentheorie. Invent. Math. 21(1–2):16–59. DOI: https://doi.org/10.1007/BF01389690.
- Neukirch, J. (1986). Class Field Theory. Berlin: Springer-Verlag.
- Sbeity, F., Sodaïgui, B. (2010). Classes de Steinitz d’extensions non abéliennes à groupe de Galois d’ordre 16 ou extraspécial d’ordre 32 et problème de plongement. Int. J. Number Theory. 6(8):1769–1783. DOI: https://doi.org/10.1142/S1793042110003794.
- Serre, J.-P. (1980). Corps Locaux, 3rd ed. Paris: Hermann.
- Smith, T. L. (1994). Extra-special groups of order 32 as Galois groups. Can. J. Math. 46(4):886–896. DOI: https://doi.org/10.4153/CJM-1994-050-2.
- Smith, T. L., Minac, J. (1991). A characterization of C-fields via Galois groups. J. Algebra 137(1):1–11. DOI: https://doi.org/10.1016/0021-8693(91)90078-M.
- Sodaïgui, B. (1988). Structure galoisienne relative des anneaux d’entiers. J. Number Theory. 28(2):189–204. DOI: https://doi.org/10.1016/0022-314X(88)90065-0.
- Sodaïgui, B. (1999). Classes de Steinitz d’extensions galoisiennes relatives de degré une puissance de 2 et problème de plongement. Illinois J. Math. 43(1):47–60. DOI: https://doi.org/10.1215/ijm/1255985336.
- Sodaïgui, B. (1999). “Galois module structure” des extensions quaternioniennes de degré 8. J. Algebra 213(2):549–556. DOI: https://doi.org/10.1006/jabr.1998.7674.
- Sodaïgui, B. (2000). Relative Galois module structure and Steinitz classes of dihedral extensions of degree 8. J. Algebra 223:367–378.
- Swan, R. G. (1962). Projective modules over group rings and maximal orders. Ann. Math. 76(1):55–61. DOI: https://doi.org/10.2307/1970264.