Loop subgroups of F_r and the image of their stabilizer subgroups in GL_r(Z)

TL;DR

This paper investigates the images of stabilizer subgroups of certain subgroups of free groups F_r under the automorphism action, providing explicit calculations for their representations in GL_r(Z).

Contribution

It introduces a method to compute the images of stabilizer subgroups of specific free group subgroups in the linear group GL_r(Z), advancing understanding of their algebraic structure.

Findings

Explicit calculations of stabilizer subgroup images in GL_r(Z)

Identification of classes of subgroups with computable images

Enhanced understanding of automorphism actions on free groups

Abstract

For a representative class of subgroups of F_r, the image of their stabilizer subgroup under the action of Aut(F_r) in GL_r(Z) is calculated.