Serwene's realizability conjecture for saturated fusion systems
Serwene's realizability conjecture for saturated fusion systems
A saturated fusion system on a finite -group is realizable if there is a finite group such that , where is a Sylow -subgroup of ; otherwise, is exotic. An -block of a finite group is a block associated with the saturated fusion system .
Serwene's conjecture. Let be a saturated fusion system. For any finite group having an -block , it follows that is realizable.
This conjecture concerns whether saturated fusion systems arising from blocks of finite groups must be realizable rather than exotic. The supplied text gives no resolution status beyond stating it as a conjecture.
Sources & referencesView supporting material
Primary source
Patrick Serwene and Constantin-Cosmin Todea, “A reduction theorem for non-vanishing of Hochschild cohomology of block algebras and Happel's property”, arXiv:2503.05432 (2025).
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