Charlotte Scott Centre for Algebra

On Tuesday the 10th of November 2020, Anitha Thillaisundaram spoke at the first series of online meetings, called “New directions in group theory and triangulated categories” and hosted virtually by the University of Manchester. Anitha spoke on Amit’s conjecture for words in finite nilpotent groups, which is joint work with Rachel Camina and Ainhoa Iniguez. The abstract of her talk is as follows:

Abstract:Let w be a word in k variables. For a finite nilpotent group G, a conjecture of Amit states that N_w(1) geq |G|^{k-1}, where N_w(1) is the number of k-tuples (g_1,…,g_k) of elements in G such that w(g_1,…,g_k)=1.This conjecture is known to be true for finite groups of nilpotency class 2. In this talk, we consider a generalized version of Amit’s conjecture and discuss known results.

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