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Papers on Free Groups 1. Pattern
Recognition Approaches to Solving Combinatorial Problems in Free Groups (with
R.M. Haralick and A.D. Miasnikov), Contemp. Math., 349, Amer. Math. Soc., In this survey paper we
present some pattern recognition techniques that can be used in studying free
groups. As an illustration we apply these methods to Whitehead minimization
problem. 2. Whitehead
method and Genetic Algorithms (with A.D. Miasnikov). Computational and experimental group
theory, 89-114, Contemp. Math., 349, Amer. Math. Soc., We describe a genetic
Whitehead's algorithm for finding minimal elements (elements of minimal
length in automorphic orbits) in arbitrary free
groups. The classical Whitehead's algorithm is extremely innefective
for free groups of big ranks, but this genetic version of it works all right.
Also we formulate several mathematical conjectures that came out of our
experiments. 3.
One Variable Equations in free groups via
context free languages (with R. Gilman). Computational and experimental group theory, 83-88, Contemp. Math., 349, Amer. Math. Soc., 4.
Automorphic
orbits in free groups (with V.Shpilrain). J.
of Algebra, 269 (2003), no. 1, 18-27. 5. Stallings
foldings and subgroups of free groups (with 6. Malnormality is decidable in free groups (with G.Baumslag and V.Remeslennikov).
Internat. Journal Algebra Comput. 9 (1999), no.6, 687-692. |