08 Fakultät Mathematik und Physik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9
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Item Open Access The discriminant embedding(2021) Döring, Svea RikeWe construct a map from the complex projective n-space into a (3(n+1)n/2-1)-dimensional sphere, called discriminant embedding. In case n = 1, the discriminant embedding is the Riemann sphere map. To show that the discriminant embedding is in fact an immersion, we calculate the determinant of a matrix resulting from its Jacobian. This is related to constructions of G. Mannoury and B. A. Fuks.Item Open Access A sieve formula for chains of p-subgroups : extending Wielandt’s proof of Sylow-Frobenius to a congruence modulo p^(ℓ+1)(2024) Schwesig, EliasGiven a finite group G and a prime p, we establish the sieve formula, which is a congruence containing as summands numbers of chains of p-subgroups of G of certain orders. This generalises the Theorem of Sylow-Frobenius. Its name stems from the sieve formula from set theory because of formal similarities.Item Open Access On twisted group rings and Galois-stable ideals(2015) Krauß, NoraLet A be a Dedekind domain with perfect field of fractions K, and let B be the integral closure of A in a finite Galois extension L of K, with Galois group G := Gal(L|K). We describe the twisted group ring B~G by means of a Wedderburn-embedding. We give a description of the image of B~G in A^(n×n) via congruences of matrix entries for an extension of the form Q(√d)|Q with d being a nonzero squarefree integer, in case of a cyclotomic field Q(ζ_p)|Q with p ∈ Z_>0 prime, and for the extensions Q(ζ_9)|Q and Q(2^{1/3}, ζ_3)|Q. By means of this description we show in examples that there are non-zero ideals in B~G that are not of the form b(B~G) for some Galois-stable ideal b ⊆ B. In case of A being a finite extension of Z, we obtain an explicit formula for the index of the image of B~G in A^(n×n) in terms of the discriminant.