in this paper, we will give necessary and sufficient conditions for certain hnnextensions of subgroup separable groups with normal associated subgroup to be conjugacyseparable. in fact, we will show that these hnn extensions are conjugacy separable if and onlyif the normalizer of one of its associated subgroup is conjugacy separable.

THE concept of HNN-extensions of groups was introduced by Higman, Neumann and Neumann in 1949. HNN-extensions and amalgamated free products have played a crucial role in combinatorial group theory, especially for algorithmic problems. In inverse semigroup theory there are many ways of constructing HNNextension in order to ensure the embeddability of the original inverse semigroup in the new one...

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 ...

3.3. The greatest common divisor and the least common multiple 12 3.4. Parabolic divisors 14 3.5. Divisibility: further properties 14 4. Normal forms arising from HNN extensions 16 4.1. HNN -normal form 16 5. Conjugacy problem 18 5.1. Conjugacy Criterion for HNN -extensions 18 5.2. Block decomposition 22 5.3. Conjugacy with respect to a subgroup 23 5.4. An algorithm for solving the Conjugacy Pr...

We consider exponent equations in finitely generated groups. These are equations, where the variables appear as exponents of group elements and take values from natural numbers. Solvability such (systems of) has been intensively studied for various classes groups recent years. In many cases, it turns out that set all solutions on an equation is a semilinear can be constructed effectively. Such ...

is called an ascending HNN extension of G (or the mapping torus of the endomorphism φ). In particular, the ascending HNN extensions of free groups of finite rank are simply the groups given by presentations 〈x1, ..., xn, t | txit−1 = wi, i = 1, ..., n〉, where w1, ..., wn are words generating a free subgroup of rank n. In [BS], Borisov and Sapir proved that all ascending HNN extensions of linear...

In this note, we give characterizations for certain HNN extensions of polycyclic-by-finite groups with central associated subgroups to be subgroup separable and conjugacy separable. We shall do this by showing the equivalence of subgroup separability and conjugacy separability in this type of HNN extensions. 2000 Mathematics Subject Classification: Primary 20E06, 20E26; Secondary 20F10, 20F19