On generalized conjugacy and some related problems

Carvalho, André

doi:10.1080/00927872.2023.2186132

Cited by 4 publications

(1 citation statement)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Kannan and Lipton had already solved in [24] the problem of deciding whether, given an n × n matrix Q of rational numbers and two vectors of rational numbers x, y ∈ Q n , there is a natural number i ∈ N such that xQ i = y, which is more general than Brinkmann's Problem for free-abelian groups. In [11], the link between Brinkmann's conjugacy problem and the conjugacy problem in cyclic extensions of the group was extended to generalized versions of the problems and in [13], the author studied a quantification of Brinkmann's problem in the context of virtually free groups.…”

Section: Introductionmentioning

confidence: 99%

On endomorphisms of the direct product of two free groups

Carvalho

2022

Journal of Group Theory

View full text Add to dashboard Cite

We describe the endomorphisms of the direct product of two free groups of finite rank and obtain conditions for which the subgroup of fixed points is finitely generated, and we do the same for periodic points. We also describe the automorphisms of such a group and solve the three Whitehead problems for automorphisms, monomorphisms and endomorphisms for groups in this class. We also obtain conditions for an endomorphism to be uniformly continuous when a suitable metric is considered and study infinite fixed points of the extension to the completion of the group.

show abstract

Section: Introductionmentioning

confidence: 99%