Displaying similar documents to “Moduli of graphs and automorphisms of free groups.”

Onθ-commutators and the corresponding non-commuting graphs

S. Shalchi, A. Erfanian, M. Farrokhi DG (2017)

Open Mathematics

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The θ-commutators of elements of a group with respect to an automorphism are introduced and their properties are investigated. Also, corresponding to θ-commutators, we define the θ-non-commuting graphs of groups and study their correlations with other notions. Furthermore, we study independent sets in θ-non-commuting graphs, which enable us to evaluate the chromatic number of such graphs.

The Automorphism Group of the Free Algebra of Rank Two

Cohn, P. (2002)

Serdica Mathematical Journal

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The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate...