Primitivity rank for random elements in free groups
نویسندگان
چکیده
Abstract For a free group F r F_{r} of finite rank ≥ 2 r\geq 2 and non-trivial element w ∈ w\in , the primitivity π ( stretchy="false">) \pi(w) is smallest subgroup H ≤ H\leq such that H
منابع مشابه
Primitivity Preserving Endomorphisms of Free Groups
An endomorphism φ of a free group is called primitivity preserving if φ takes every primitive element to another primitive. In this paper we prove that every primitivity preserving endomorphism of a free group of a finite rank n ≥ 3 is an automorphism.
متن کاملEnumerating Palindromes in Rank Two Free Groups
Conjugacy classes of primitive words in the free group of rank two can indexed by the rationals. A representative for each conjugacy class is given by a recursive enumeration scheme and the representative, usually called a Farey word, is denoted by Wp/q where p and q are relatively prime integers. Primitive pairs, that is, pairs of words that generate the free group, correspond to pairs of word...
متن کاملTest Words, Generic Elements and Almost Primitivity
A test element in a group G is an element g with the property that if f(g) = g for an endomorphism f of G to G then f must be an automorphism. A test element in a free group is called a test word. Nielsen gave the first example of a test word by showing that in the free group on x, y the commutator [x, y] satisfies this property. T. Turner recently characterized test words as those elements of ...
متن کاملGenerating Random Elements in Finite Groups
Let G be a finite group of order g. A probability distribution Z on G is called ε-uniform if |Z(x) − 1/g| ≤ ε/g for each x ∈ G. If x1, x2, . . . , xm is a list of elements of G, then the random cube Zm := Cube(x1, . . . , xm) is the probability distribution where Zm(y) is proportional to the number of ways in which y can be written as a product x1 1 x ε2 2 · · · xεm m with each εi = 0 or 1. Let...
متن کاملRandom walks on finite rank solvable groups
Abstract. We establish the lower bound p2t(e, e) exp(−t1/3), for the large times asymptotic behaviours of the probabilities p2t(e, e) of return to the origin at even times 2t, for random walks associated with finite symmetric generating sets of solvable groups of finite Prüfer rank. (A group has finite Prüfer rank if there is an integer r , such that any of its finitely generated subgroup admit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2022
ISSN: ['1435-4446', '1433-5883']
DOI: https://doi.org/10.1515/jgth-2021-0150