Finitely generated subgroups of amalgamated free products and HNN groups

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Positive theories of HNN-extensions and amalgamated free products

It is shown that the positive first-order theory of an HNN-extension G = 〈H, t; tat = φ(a)(a ∈ A)〉 can be reduced to the existential firstorder theory of G provided that A and B are proper subgroups of the base group H with A∩B finite. For an amalgamated free product G = H ∗A J , we show that the positive first-order theory of G can be reduced to the existential first-order theory of G in case ...

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ژورنال

عنوان ژورنال: Journal of the Australian Mathematical Society

سال: 1976

ISSN: 1446-7887,1446-8107

DOI: 10.1017/s1446788700014737