On the abelianization of certain groups of formal power series

2024/07/19 by Pavez-Cornejo, Javier
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2407.14019

Abstract

We compute the abelianization of the Jennings group J_k(ℤ) of powers series with constant coefficient 0, linear coefficent equal to 1 and vanishing coefficients in orders greater or equal than 2 and less than k, where k\geqslant2. This is accomplished by directly dealing with the equivalence classes in the corresponding abelianizations, in contrast with the work of I. K. Babenko and S. A. Bogatyy, who give an explicit abelianization morphism for the case k=2.

Related

• The abelianization of SL₂(ℤ[(1)/(m)])
• DIAGRAMS OF AN ABELIAN GROUP
• Classifying abelian groups through acyclic matchings
• Elements of Finite Order in the Group of Formal Power Series Under Composition
• Irreducibility in generalized power series