4 papers · 1 filter
Topological isomorphism of procountable groups is universal analytic
Xinan Dai, Wenhao Deng, Yingdong Shi +2
We prove that topological isomorphism of procountable groups is a universal analytic equivalence relation, answering a question of Gao, Nies, and Paolini. The same conclusion follo…
Centralizer Excess as an Obstruction to Carlson's Depth Conjecture
Xinan Dai, Kuok Fai Chao
Let and . The cohomology ring has depth two, and we prove that the minimum quotient dimension of an associated pri…
A Finite E-Group of Nilpotency Class Three
Xinan Dai, Wenhao Deng, Yidong Shi +2
A group is an E-group if every element commutes with each of its endomorphic images. Caranti asked whether a finite E-group can have nilpotency class three. We prove that the -g…
An Exact Counterexample to Carlson's Associated-Prime Depth Conjecture from a Group of Order 128
Xinan Dai, Wenhao Deng, Yingdong Shi +2
In Question~3.1 of his 1995 paper on depth and transfer, Carlson asked whether the depth of a finite-group cohomology ring is always realized by the dimension of one of its associa…