Separable Subsets of GFERF Negatively Curved Groups

关于自由循环群和管状群的一些问题

Some questions related to free-by-cyclic groups and tubular groups

本文研究自由循环管状群的特殊性、虚拟作用及循环子群可分离性，否定多个相关猜想并提供反例。

Productivity of sequences with respect to a given weight function

Given a function f: N --> (omega+1)-{0}, we say that a faithfully indexed sequence {a_n: n in N} of elements of a topological group G is: (i) f-Cauchy productive (f-productive) provided that the sequence {prod_{n=0}^m a_n^{z(n)}: m in N} is left Cauchy (converges to some element of G, respectively) for each function z: N --> Z such that |z(n)| <= f(n) for every n in N; (ii) unconditionally f-Cauchy productive (unconditionally f-productive) provided that the sequence {a_{s(n)}: n in N\} is (f\circ s)-Cauchy productive (respectively, (f\circ s)-productive) for every bijection s: N --> N. (Biject…