Graduate Seminar

Location:  RI 208

Speaker: Agustin D'Alessandro

MSc Student supervised by Fernando Szechtman

Title:  Presentations of some \(p\)-groups

Abstract:

In a previous talk, we introduced the group of formal power series in one variable with coefficients in a commutative ring with identity \(R\) under the substitution operation and discussed some known results. In this lecture we focus on the finite \(p\)-groups \(G_n(\mathbb{Z}/p\mathbb{Z})\), where the operation is substitution followed by truncation, and find a power-commutator presentation (PCP) of these groups. 

In order to obtain a PCP, we studied the commutator and \(p\)-power structure of \(G_n(\mathbb{Z}/p\mathbb{Z})\) and obtained new results on both. We show how these formulas apply to the generators of \(G_n(\mathbb{Z}/p\mathbb{Z})\) and use them to obtain a PCP of these groups, as well as further structural information about them.