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math.GR2026
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…
math.GR2026
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…
math.GR2026
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…