Splendid Morita equivalences for principal blocks with semidihedral defect groups

TL;DR

This paper classifies principal blocks with semidihedral defect groups up to splendid Morita equivalence, completing the classification for tame type blocks and confirming Puig's Finiteness Conjecture for these cases.

Contribution

It provides a complete classification of principal blocks with semidihedral defect groups up to splendid Morita equivalence and verifies Puig's Finiteness Conjecture for these blocks.

Findings

Complete classification of principal blocks with semidihedral defect groups

Puig's Finiteness Conjecture holds for these blocks

Advances understanding of tame representation type blocks

Abstract

We classify principal blocks of finite groups with semidihedral defect groups up to splendid Morita equivalence. This completes the classification of all principal $2$-blocks of tame representation type up to splendid Morita equivalence and shows that Puig's Finiteness Conjecture holds for such blocks.