U. of Haifa Algebra seminar, November 19, 2020
Algebra Seminar
Speaker: Manoj K. Yadav (Harish-Chandra Research Institute)
Topic: Surjectivity of commutator map for finite $p$-groups
Place: This is an online seminar. Please email Yuval Ginosar “ginosar at math dot haifa dot ac dot il” for the Zoom ID and password.
Date: Thursday, November 19, 2020
Time: 12:00
Abstract:
For a group $G$, the map $\alpha : G \times G \to \gamma_2(G)$, defined by $\alpha(x, y) = x^{-1}y^{-1}xy$, is call the commutator map for $G$. Various aspects of commutator map for finite groups have been investigated by many mathematicians in the past. The most sought after aspect, perhaps, is the surjectivity. The proof of the famous Ore’s conjecture establishes the surjectivity of the commutator map for finite simple groups. The same is true for almost all finite quasisimple groups. Many other classes of finite groups, including $p$-groups, have been investigated. My motive in this talk is to report some recent developments on this topic and present a detailed exposition on the commutator map for finite $p$-groups.
