The Automorphism Group of a Hypercube
نویسنده
چکیده
We present explicitly in this expository note the automorphism group of the hypercube Qd of dimension d as a permutation group acting on its 2 d nodes. This group (Qd) acts on the node set Vd of Qd and thus has degree 2 . It is expressed as the binary operation called exponentiation which combines the two symmetric groups S2 (of degree and order 2) and Sd (of degree d and order d!). Speci cally,
منابع مشابه
A Note on Automorphisms of the Infinite-Dimensional Hypercube Graph
We define the infinite-dimensional hypercube graph Hא0 as the graph whose vertex set is formed by the so-called singular subsets of Z \ {0}. This graph is not connected, but it has isomorphic connected components. We show that the restrictions of its automorphisms to the connected components are induced by permutations on Z \ {0} preserving the family of singular subsets. As an application, we ...
متن کاملLatin k-hypercubes
We study k dimensional Latin hypercubes of order n. We describe the automorphism groups of the hypercubes and define the parity of a hypercube and relate the parity with the determinant of a permutation hypercube. We determine the parity in the orbits of the automorphism group. Based on this definition of parity we make a conjecture similar to the Alon-Tarsi conjecture. We define an orthogonali...
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 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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. UCS
دوره 6 شماره
صفحات -
تاریخ انتشار 2000