Coset complexes of 𝑝-subgroups in finite groups

Abstract Let 𝐺 be a finite group and 𝑝 a prime. We denote by <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi mathvariant="script">C</m:mi> <m:mi>p</m:mi> </m:msub> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>G</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> \mathscr{C}_{p}(G) the poset of all cosets of 𝑝-subgroups of 𝐺. We characterize the homotopy type of the geometric realization <m:math xmlns:m="http://www.w3.org/1998/Ma