2 citations · 3 across the 9 of their papers we have counts for
6 papers · 1 filter
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…
Multiplicative measures on free groups
Alexandre V. Borovik, Alexei G. Myasnikov, Vladimir N. Remeslennikov
We introduce a family of atomic measures on free groups generated by no-return random walks. These measures are shown to be very convenient for comparing "relative sizes" of subgro…
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…
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…
Stallings foldings and the subgroup structure of free groups
Ilya Kapovich, Alexei Myasnikov
We re-cast in a more combinatorial and computational form the foldings approach of John Stallings and pursue a detailed study of the subgroup structure of free groups. In particula…