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9781470467234 Academic Inspection Copy

The Generation Problem in Thompson Group $F$

  • ISBN-13: 9781470467234
  • Publisher: AMERICAN MATHEMATICAL SOCIETY
    Imprint: AMERICAN MATHEMATICAL SOCIETY
  • By Gili Golan Polak
  • Price: AUD $219.00
  • Stock: 0 in stock
  • Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
  • Local release date: 29/06/2024
  • Format: Paperback (254.00mm X 178.00mm) 94 pages Weight: 272g
  • Categories: Algebra [PBF]Algebraic geometry [PBMW]
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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.
Gili Golan Polak, Ben Gurion University of the Negev, Be'er Sheva, Israel.
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