2 citations · 9 across the 13 of their papers we have counts for
5 papers · 2 filters
Automorphic orbits in free groups
Alexei G. Myasnikov, Vladimir Shpilrain
Let be the free group of a finite rank . We study orbits , where is an element of the group , under the action of an automorphism . If an orbit like…
Average-case complexity and decision problems in group theory
Ilya Kapovich, Alexei Myasnikov, Paul Schupp +1
We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on ``generic…
Measuring sets in infinite groups
Alexandre V. Borovik, Alexei G. Myasnikov, Vladimir Shpilrain
We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a…
Representing braids by automorphisms
Vladimir Shpilrain
Based on a normal form for braid group elements suggested by Dehornoy, we prove several representations of braid groups by automorphisms of a free group to be faithful. This includ…
Generic-case complexity, decision problems in group theory and random walks
Ilya Kapovich, Alexei Myasnikov, Paul Schupp +1
We give a precise definition of ``generic-case complexity'' and show that for a very large class of finitely generated groups the classical decision problems of group theory - the…