Year: 2025
Type: preprint
Abstract: Kropholler's operation ${\scriptstyle{\bf LH}}$ and Talelli's operation $Φ$ can be often used to formally enlarge the class of available examples of groups that satisfy certain homological conditions. In this paper, we employ this enlargement technique regarding two specific homological conditions. We thereby demonstrate the abundance of groups that (a) have virtually Gorenstein group algebras, as defined by Beligiannis and Reiten, and (b) satisfy Moore's conjecture on the relation between projectivity and relative projectivity, that was studied by Chouinard, Aljadeff, Cornick, Ginosar, Kropholler and Meir.
Source: arXiv (Cornell University)
Authors: Emmanouil, Ioannis, Ren, Wei
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G1379959802
OpenAlex ID: W6979372529
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