The Free Group of Rank 2 Is a Limit of Thompson’s Group F
نویسنده
چکیده
From [9], an n-marked group is a pair (G,S) where S is an ordered n-tuple of generators (the n-marking) of the group G. An isomorphism of marked groups must preserve the markings. With Gn the set of all isomorphism classes of n-marked groups, one says that two elements of Gn are no more than e −R apart if they have satisfy the same relations of length no longer than R. This gives a metric on Gn, and a group L is a G-limit if it is a limit in Gn of a sequence of marked groups each of which is isomorphic as an unmarked group to G. Marked groups and their limits are defined and studied in [5] where, among other things, it is shown that Gn is compact. Limits of marked groups extend the notion of limit groups of [8]. Groups that cannot be obtained as a limit of Thompson’s group F are studied in [9]. Recently Akhmedov, Stein and Taback have announced that the free group on 3 generators is a limit of 3-markings of Thompson’s group F . The purpose of this paper is to prove the following.
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