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For any number field $K$ with non-elementary $3$ -class group ${Cl}_{3} (K) ≃ C_{3^{e}} \times C_{3}$ , $e \geq 2$ , the punctured capitulation type $ϰ (K)$ of $K$ in its unramified cyclic cubic extensions $L_{i}$ , $1 \leq i \leq 4$ , is an orbit under the action of $S_{3} \times S_{3}$ . By means of Artin’s reciprocity law, the arithmetical invariant $ϰ (K)$ is translated to the punctured transfer kernel type $ϰ (G_{2})$ of the automorphism group $G_{2} = Gal (F_{3}^{2} (K) / K)$ of the second Hilbert $3$ -class field of $K$ . A classification of finite $3$ -groups $G$ with low order and bicyclic commutator quotient $G / G^{'} ≃ C_{3^{e}} \times C_{3}$ , $2 \leq e \leq 6$ , according to the algebraic invariant...

Blocks, solvable permutation groups, and Landau's theorem.

Burkhard Külshammer (1989)

Journal für die reine und angewandte Mathematik

Blocks, Vertices and Normal Subgroups.

Reinhard Knörr (1976)

Mathematische Zeitschrift

Blocks with Dihedral Defect Groups in Solvable Groups.

Gerhard O. Michler, Karin Erdmann (1977)

Mathematische Zeitschrift

Breaking points in the poset of conjugacy classes of subgroups of a finite group

Marius Tărnăuceanu (2019)

Czechoslovak Mathematical Journal

We determine the finite groups whose poset of conjugacy classes of subgroups has breaking points. This leads to a new characterization of the generalized quaternion $2$ -groups. A generalization of this property is also studied.

Buildings and shadows.

Betti Salzberg (1982)

Aequationes mathematicae

Burnside obstructions to the Montesinos-Nakanishi 3-move conjecture.

Dabkowski, Mieczysław K., Przytycki, Józef H. (2002)

Geometry & Topology

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