Year: 2026
Type: preprint
Abstract: We prove that any block of a profinite group with a topologically finitely generated defect group $D$ is isomorphic to a block of a virtually pro-$p$ group, and if $D$ is finitely presented then so is the basic algebra of the block over $k$. Using these general results we then prove that any block with defect group $D=\mathbb Z_p^n$ is Morita equivalent to $\mathcal O_α[[\mathbb Z_p^n\rtimes E]]$ for a finite $p'$-group $E$ acting faithfully and a $2$-cocycle $α\in H^2(E,k^\times)$. In particular, Donovan's conjecture holds for such blocks of profinite groups.
Source: arXiv (Cornell University)
Authors: Eisele, Florian, MacQuarrie, John W.
Institution: University of Manchester
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214802547