The order complex of cosets in a finite group

Speaker:  Prof. MENG Hangyang (Shanghai University)

Venue: 203, Building 2, Haina Court, Zijingang Campus

Abstract: In this talk, we will introduce some algebraic topology methods on studying the poset(=partial ordered set) of some cosets of a finite group. Let G be a finite group and X be a subgroup of G. We investigate the topological properties of poset C_X(G) of cosets Hx in G with X ≤ H < G. We show that C_X(G) is non-contracitble if G is solvable or N_G(X) contains a Sylow 2-subgroup and a Sylow 3-subgroup of G. This result follows J. Shareshian and R. Woodroofe’s work in Adv. Math(2016). We also gives some divisi[1]bility properties of the Euler characteristic of C_X(G) when X is a p-group, which follows K. S. Brown’s classical result in J.Algebra(2000).