منابع مشابه
A characterization of the symmetric group of prime degree
Let $G$ be a finite group and $Gamma(G)$ the prime graph of $G$. Recently people have been using prime graphs to study simple groups. Naturally we pose a question: can we use prime graphs to study almost simple groups or non-simple groups? In this paper some results in this respect are obtained and as follows: $Gcong S_p$ if and only if $|G|=|S_p|$ and $Gamma(G)=Gamma(S_p)$, whe...
متن کاملSubgroups of the Symmetric Group
We started our research with the intent on answering the following question: can we find a way to calculate all the subgroups of the symmetric group. This is easier said that done, as the number of subgroups for a symmetric group grows quickly with each successive symmetric group. This problem can actually be simplified to finding the subgroup conjugacy classes. So now we have the slightly diff...
متن کاملNotes on the symmetric group
Recall that, given a set X, the set SX of all bijections from X to itself (or, more briefly, permutations of X) is group under function composition. In particular, for each n ∈ N, the symmetric group Sn is the group of permutations of the set {1, . . . , n}, with the group operation equal to function composition. Thus Sn is a group with n! elements, and it is not abelian if n ≥ 3. If X is a fin...
متن کاملa characterization of the symmetric group of prime degree
let $g$ be a finite group and $gamma(g)$ the prime graph of $g$. recently people have been using prime graphs to study simple groups. naturally we pose a question: can we use prime graphs to study almost simple groups or non-simple groups? in this paper some results in this respect are obtained and as follows: $gcong s_p$ if and only if $|g|=|s_p|$ and $gamma(g)=gamma(s_p)$, whe...
متن کاملcharacterization of the symmetric group by its non-commuting graph
the non-commuting graph $nabla(g)$ of a non-abelian group $g$ is defined as follows: its vertex set is $g-z(g)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. in this paper we 'll prove that if $g$ is a finite group with $nabla(g)congnabla(bs_{n})$, then $g cong bs_{n}$, where $bs_{n}$ is the symmetric group of degre...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1991
ISSN: 0001-8708
DOI: 10.1016/0001-8708(91)90013-w