Subgroup theorem for valuated groups and the CSA property

TL;DR

This paper investigates valuated groups with normal forms, proving a subgroup theorem similar to Grushko-Neumann's and exploring the CSA property within these groups.

Contribution

It introduces a subgroup theorem for valuated groups with normal forms and analyzes the CSA property in this context.

Findings

Proved a subgroup theorem analogous to Grushko-Neumann's

Studied the CSA property in valuated groups with normal forms

Abstract

A valuated group with normal forms is a group with an integer-valued length function satisfying some Lyndon's axioms and an additional axiom considered by Hurley. We prove a subgroup theorem for valuated groups with normal forms analogous to Grushko-Neumann's theorem. We study also the CSA property in such groups.