The Automorphism Group of a Shift of Subquadratic Growth
نویسندگان
چکیده
For a subshift over a finite alphabet, a measure of the complexity of the system is obtained by counting the number of nonempty cylinder sets of length n. When this complexity grows exponentially, the automorphism group has been shown to be large for various classes of subshifts. In contrast, we show that subquadratic growth of the complexity implies that for a topologically transitive shift X, the automorphism group Aut(X) is small: if H is the subgroup of Aut(X) generated by the shift, then Aut(X)/H is periodic.
منابع مشابه
The Automorphism Group of a Shift of Subquadratic Growth
For a subshift over a finite alphabet, a measure of the complexity of the system is obtained by counting the number of nonempty cylinder sets of length n. When this complexity grows exponentially, the automorphism group has been shown to be large for various classes of subshifts. In contrast, we show that subquadratic growth of the complexity implies that for a topologically transitive shift X,...
متن کاملThe Automorphism Group of a Minimal Shift of Stretched Exponential Growth
The group of automorphisms of a symbolic dynamical system is countable, but often very large. For example, for a mixing subshift of finite type, the automorphism group contains isomorphic copies of the free group on two generators and the direct sum of countably many copies of Z. In contrast, the group of automorphisms of a symbolic system of zero entropy seems to be highly constrained. Our mai...
متن کاملAutomorphism Group of a Possible 2-(121, 16, 2) Symmetric Design
Let D be a symmetric 2-(121, 16, 2) design with the automorphism group of Aut(D). In this paper the order of automorphism of prime order of Aut(D) is studied, and some results are obtained about the number of fixed points of these automorphisms. Also we will show that |Aut(D)|=2p 3q 5r 7s 11t 13u, where p, q, r, s, t and u are non-negative integers such that r, s, t, u ? 1. In addition we prese...
متن کاملNILPOTENCY AND SOLUBILITY OF GROUPS RELATIVE TO AN AUTOMORPHISM
In this paper we introduce the concept of α-commutator which its definition is based on generalized conjugate classes. With this notion, α-nilpotent groups, α-solvable groups, nilpotency and solvability of groups related to the automorphism are defined. N(G) and S(G) are the set of all nilpotency classes and the set of all solvability classes for the group G with respect to different automorphi...
متن کاملOn the nilpotency class of the automorphism group of some finite p-groups
Let $G$ be a $p$-group of order $p^n$ and $Phi$=$Phi(G)$ be the Frattini subgroup of $G$. It is shown that the nilpotency class of $Autf(G)$, the group of all automorphisms of $G$ centralizing $G/ Fr(G)$, takes the maximum value $n-2$ if and only if $G$ is of maximal class. We also determine the nilpotency class of $Autf(G)$ when $G$ is a finite abelian $p$-group.
متن کامل