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Bicyclic commutator quotients with one non-elementary component

Daniel Mayer (2023)

Mathematica Bohemica

For any number field K with non-elementary 3 -class group Cl 3 ( K ) C 3 e × C 3 , e 2 , the punctured capitulation type ϰ ( K ) of K in its unramified cyclic cubic extensions L i , 1 i 4 , is an orbit under the action of S 3 × 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 × C 3 , 2 e 6 , according to the algebraic invariant...

C 55 -groups.

Dolfi, Silvio, Jabara, Enrico, Lucido, Maria Silvia (2004)

Sibirskij Matematicheskij Zhurnal

Central sequences in the factor associated with Thompson’s group F

Paul Jolissaint (1998)

Annales de l'institut Fourier

We prove that the type II 1 factor L ( F ) generated by the regular representation of F is isomorphic to its tensor product with the hyperfinite type II 1 factor. This implies that the unitary group of L ( F ) is contractible with respect to the topology defined by the natural Hilbertian norm.

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