{"product_id":"9781470467234-the-generation-problem-in-thompson","title":"The Generation Problem in Thompson Group $F$","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003eWe 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.\u003cbr\u003eWe 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.\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":54845443113334,"sku":"9781470467234","price":68.38,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/orig_36044281_3d638495-6866-48d3-a9df-c7ad511f5816.jpg?v=1757580470","url":"https:\/\/www.rarewaves.com\/products\/9781470467234-the-generation-problem-in-thompson","provider":"Rarewaves.com","version":"1.0","type":"link"}