Rank Gradient andp-gradient of Amalgamated Free Products and HNN Extensions
نویسندگان
چکیده
منابع مشابه
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 ...
متن کاملTheories of HNN-Extensions and Amalgamated Products
It is shown that the existential theory of G with rational constraints, over an HNN-extension G = 〈H, t; tat = φ(a)(a ∈ A)〉 is decidable, provided that the same problem is decidable in the base group H and that A is a finite group. The positive theory of G is decidable, provided that the existential positive theory of G is decidable and that A and φ(A) are proper subgroups of the base group H w...
متن کاملRational Subsets in HNN-Extensions and Amalgamated Products
of a group H, where A and B are isomorphic subgroups of H and φ : A → B is an isomorphism, results from adding to H a new generator t such that the conjugation of the subgroup A ≤ H by t realizes the isomorphism φ. We also say that A and B in (2) are the associated subgroups. One of the first important applications of HNN-extensions was a more transparent proof of the celebrated result of Novik...
متن کاملKnapsack in Graph Groups, HNN-Extensions and Amalgamated Products
It is shown that the knapsack problem, which was introduced by Myasnikov et al. for arbitrary finitely generated groups, can be solved in NP for graph groups. This result even holds if the group elements are represented in a compressed form by SLPs, which generalizes the classical NP-completeness result of the integer knapsack problem. We also prove general transfer results: NP-membership of th...
متن کاملA Relationship between Hnn Extensions and Amalgamated Free Products in Operator Algebras
By improving the previous construction in [18] we observe that any reduced HNN extension is a corner of a certain reduced amalgamated free product in both the von Neumann algebra and the C∗-algebra settings. Then, the same fact is shown for universal HNN extensions of C∗-algebras. We apply the observation to the questions of factoriality and type classification of HNN extensions of von Neumann ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2015
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2014.948631