Coset complexes of 𝑝-subgroups in finite groups

Key Points

• To characterize the homotopy type of coset complexes associated with p-subgroups in finite groups and establish properties of Euler characteristics.
• Characterization of the poset of cosets of p-subgroups in a finite group G.
• Analysis of the homotopy type and geometric realization of these cosets.
• Investigation of Euler characteristics for specific classes of finite groups.
• The Euler characteristic of coset complexes for p-closed groups yields a specific formula.
• It was found that χ(Cp(G)) equals |G|_{p'} for certain finite groups.
• The congruence χ(Cp(G)) ≡ |G|_{p'} (mod p) holds for all groups G.