We show that the generation problem in Thompson's group F is decidable, i.e., there is an algorithm which decides if a finite set of elements of F generates the whole F. The algorithm makes use of the Stallings 2-core of subgroups of F, which can be defined in an analogous way to the Stallings core of subgroups of a finitely generated free group. Further study of the Stallings 2-core of subgroups of F provides a solution to another algorithmic problem in F. Namely, given a finitely generated subgroup H of F, it is decidable if H acts transitively on the set of finite dyadic fractions D. Other applications of the study include the construction of new maximal subgroups of F of infinite index, among which, a maximal subgroup of infinite index which acts transitively on the set D and the construction of an elementary amenable subgroup of F which is maximal in a normal subgroup of F.

About the Author
Gili Golan Polak, Ben Gurion University of the Negev, Be'er Sheva, Israel.


Book Information
ISBN 9781470467234
Author Gili Golan Polak
Format Paperback
Page Count 94
Imprint American Mathematical Society
Publisher American Mathematical Society
Weight(grams) 272g