Extending Partial Automorphisms and the Profinite Topology on Free Groups
نویسندگان
چکیده
A class of structures C is said to have the extension property for partial automorphisms (EPPA) if, whenever C1 and C2 are structures in C, C1 finite, C1 ⊆ C2, and p1, p2, . . . , pn are partial automorphisms of C1 extending to automorphisms of C2, then there exist a finite structure C3 in C and automorphisms α1, α2, . . . , αn of C3 extending the pi. We will prove that some classes of structures have the EPPA and show the equivalence of these kinds of results with problems related with the profinite topology on free groups. In particular, we will give a generalisation of the theorem, due to Ribes and Zalesskĭı stating that a finite product of finitely generated subgroups is closed for this topology.
منابع مشابه
Extending Partial Automorphisms and the Proonite Topology on Free Groups
A class of structures C is said to have the extension property for partial automorphisms (EPPA) if, whenever C 1 and C 2 are structures in C, C 1 nite, C 1 C 2 , and p 1 , p 2 , : : :, p n are partial automorphisms of C 1 extending to automorphisms of C 2 , then there exist a nite structure C 3 in C and automorphisms 1 , 2 , : : :, n of C 3 extending the p i. We will prove that some classes of ...
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