Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFixed points and stable images of endomorphisms for the free group of rank two
92
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We give an algorithm which computes the fixed subgroup and the stable image for any endomorphism of the free group of rank two $F_2$, answering for $F_2$ a question posed by Stallings in 1984 and a question of Ventura.
rate research
Read More
We prove that the automorphism group of the braid group on four strands acts faithfully and geometrically on a CAT(0) 2-complex. This implies that the automorphism group of the free group of rank two acts faithfully and geometrically on a CAT(0) 2-complex, in contrast to the situation for rank three and above.
The present paper records more details of the relationship between primitive elements and palindromes in F_2, the free group of rank two. We characterise the conjugacy classes of primitive elements which contain palindromes as those which contain cyclically reduced words of odd length. We identify large palindromic subwords of certain primitives in conjugacy classes which contain cyclically reduced words of even length. We show that under obvious conditions on exponent sums, pairs of palindromic primitives form palindromic bases for F_2. Further, we note that each cyclically reduced primitive element is either a palindrome, or the concatenation of two palindromes.
We outline a separable matrix ansatz for the potentials in effective field theories of nonrelativistic two-body systems with short-range interactions. We use this ansatz to construct new fixed points of the renormalisation-group equation for these potentials. New fixed points indicate a much richer structure than previously recognized in the RG flows of simple short-range potentials.
The main result of the paper is the following theorem. Let $q$ be a prime and $A$ an elementary abelian group of order $q^3$. Suppose that $A$ acts coprimely on a profinite group $G$ and assume that $C_G(a)$ is locally nilpotent for each $ain A^{#}$. Then the group $G$ is locally nilpotent.
We continue our study of residual properties of mapping tori of free group endomorphisms. In this paper, we prove that each of these groups are virtually residually (finite $p$)-groups for all but finitely many primes$p$. The method involves further studies of polynomial maps over finite fields and $p$-adic completions of number fields.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
