Every finite group is the automorphism group of some perfect code
نویسندگان
چکیده
منابع مشابه
Every Finite Group Is the Automorphism Group of Some Finite Orthomodular Lattice
If L is a lattice, the automorphism group of L is denoted Aut(L). It is known that given a finite abstract group H, there exists a finite distributive lattice D such that Aut(D) £= H. It is also known that one cannot expect to find a finite orthocomplemented distributive (Boolean) lattice B such that Aut(B) s= H. In this paper it is shown that there does exist a finite orthomodular lattice L su...
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Let G = (V,E) be a simple graph with exactly n vertices and m edges. The aim of this paper is a new method for investigating nontriviality of the automorphism group of graphs. To do this, we prove that if |E| >=[(n - 1)2/2] then |Aut(G)|>1 and |Aut(G)| is even number.
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 کاملThe Automorphism Group of a Finite p-Group is Almost Always a p-Group
Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups whose automorphism group is a p-group. Yet the goal of this paper is to prove that the automorphism group of a finite p-group is almost always a p-group. The asymptotics in our theorem involve fixing any two of the following parameters and letting the thir...
متن کاملThe Automorphism Group of Commuting Graph of a Finite Group
Let G be a finite group and X be a union of conjugacy classes of G. Define C(G,X) to be the graph with vertex set X and x, y ∈ X (x 6= y) joined by an edge whenever they commute. In the case that X = G, this graph is named commuting graph of G, denoted by ∆(G). The aim of this paper is to study the automorphism group of the commuting graph. It is proved that Aut(∆(G)) is abelian if and only if ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1986
ISSN: 0097-3165
DOI: 10.1016/0097-3165(86)90021-x