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Dual-standard subgroups in nonperiodic locally soluble groups

Stewart E. Stonehewer, Giovanni Zacher (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let G be a non-periodic locally solvable group. A characterization is given of the subgroups-D of G for which the map X X D , for all X G , defines a lattice-endomorphism.

Elementary embeddings in torsion-free hyperbolic groups

Chloé Perin (2011)

Annales scientifiques de l'École Normale Supérieure

We describe first-order logic elementary embeddings in a torsion-free hyperbolic group in terms of Sela’s hyperbolic towers. Thus, if H embeds elementarily in a torsion free hyperbolic group Γ , we show that the group Γ can be obtained by successive amalgamations of groups of surfaces with boundary to a free product of  H with some free group and groups of closed surfaces. This gives as a corollary that an elementary subgroup of a finitely generated free group is a free factor. We also consider the...

Embedding orders into central simple algebras

Benjamin Linowitz, Thomas R. Shemanske (2012)

Journal de Théorie des Nombres de Bordeaux

The question of embedding fields into central simple algebras B over a number field K was the realm of class field theory. The subject of embedding orders contained in the ring of integers of maximal subfields L of such an algebra into orders in that algebra is more nuanced. The first such result along those lines is an elegant result of Chevalley [6] which says that with B = M n ( K ) the ratio of the number of isomorphism classes of maximal orders in B into which the ring of integers of L can be embedded...

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