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On the graded quotients of the ring of Fricke characters of a free group
Ring of Fricke characters Automorphism groups of free groups Andreadakis-Johnson filtration
2012/6/27
First, we study a descending filtration of the ring of Fricke characters of a free group consisting of ideals on which the automorphism group of a free group acts. Then using it, we define a descendin...
Free group algebras in Malcev-Neumann skew fields of fractions
Division rings Malcev-Neumann series Rings and Algebras
2011/9/5
Abstract: Let K be a skew field and (G,<) an ordered group. We show that the skew field generated by the group ring K[G] inside the Malcev-Neumann series ring K((G;<)) contains noncommutative free gro...
Explicit computation of the index of a positive outer automorphism of the free group
Explicit computation index of positive outer automorphism
2011/2/21
We give an algorithm for finding the index of a positive outer au-tomorphism of the free group, and prove the algorithm exits in a finite time.