Order complexes of coset posets of finite groups are not contractible
Abstract
We show that the order complex of the poset of all cosets of all proper subgroups of a finite group G is never F2-acyclic and therefore never contractible. This settles a question of K. S. Brown.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.