منابع مشابه
On groups and fields interpretable in torsion-free hyperbolic groups
We prove that the generic type of a non-cyclic torsion-free hyperbolic group G is foreign to any interpretable abelian group, hence also to any interpretable field. This result depends, among other things, on the definable simplicity of a non-cyclic torsion-free hyperbolic group, and we take the opportunity to give a proof of the latter using Sela’s description of imaginaries in torsion-free hy...
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The equivalence relation isoclinism partitions the class of all pairs of groups into families. In this paper, a complete classification of the set of all pairs $(G,G')$ is established, whenever $G$ is a $p$-group of order at most $p^5$ and $p$ is a prime number greater than 3. Moreover, the classification of pairs $(H,H')$ for extra special $p$-groups $H$ is also given.
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We generalize the notion of a projective profinite group to a projective pair of a profinite group and a closed subgroup. We establish the connection with Pseudo Algebraically Closed (PAC) extensions of PAC fields: Let M be an algebraic extension of a PAC field K. Then M/K is PAC if and only if the corresponding pair of absolute Galois groups (Gal(M),Gal(K)) is projective. Moreover any projecti...
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2017
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-017-0565-4