Recognition of the groups L 5(4) and U 4(4) by the prime graph
نویسندگان
چکیده
منابع مشابه
Recognition of the group $G_2(5)$ by the prime graph
Let $G$ be a finite group. The prime graph of $G$ is a graph $Gamma(G)$ with vertex set $pi(G)$, the set of all prime divisors of $|G|$, and two distinct vertices $p$ and $q$ are adjacent by an edge if $G$ has an element of order $pq$. In this paper we prove that if $Gamma(G)=Gamma(G_2(5))$, then $G$ has a normal subgroup $N$ such that $pi(N)subseteq{2,3,5}$ and $G/Nequiv G_2(5)$.
متن کامل2-recognizability of the simple groups $B_n(3)$ and $C_n(3)$ by prime graph
Let $G$ be a finite group and let $GK(G)$ be the prime graph of $G$. We assume that $ngeqslant 5 $ is an odd number. In this paper, we show that the simple groups $B_n(3)$ and $C_n(3)$ are 2-recognizable by their prime graphs. As consequences of the result, the characterizability of the groups $B_n(3)$ and $C_n(3)$ by their spectra and by the set of orders of maximal abelian subgroups are ...
متن کامل2-quasirecognizability of the simple groups B_n(p) and C_n(p) by prime graph
Let G be a finite group and let $GK(G)$ be the prime graph of G. We assume that $n$ is an odd number. In this paper, we show that if $GK(G)=GK(B_n(p))$, where $ngeq 9$ and $pin {3,5,7}$, then G has a unique nonabelian composition factor isomorphic to $B_n(p)$ or $C_n(p)$ . As consequences of our result, $B_n(p)$ is quasirecognizable by its spectrum and also by a new proof, the ...
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Vasil'ev posed Problem 16.26 in [The Kourovka Notebook: Unsolved Problems in Group Theory, 16th ed.,Sobolev Inst. Math., Novosibirsk (2006).] as follows:Does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphicnonabelian finite simple groups with the same graphs of primes? Conjecture: $k = 5$.In [Zvezdina, On nonabelian simple groups having the same prime graph a...
متن کاملRecognition by prime graph of the almost simple group PGL(2, 25)
Throughout this paper, every groups are finite. The prime graph of a group $G$ is denoted by $Gamma(G)$. Also $G$ is called recognizable by prime graph if for every finite group $H$ with $Gamma(H) = Gamma(G)$, we conclude that $Gcong H$. Until now, it is proved that if $k$ is an odd number and $p$ is an odd prime number, then $PGL(2,p^k)$ is recognizable by prime graph. So if $k$ is even, the r...
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ژورنال
عنوان ژورنال: Ukrainian Mathematical Journal
سال: 2012
ISSN: 0041-5995,1573-9376
DOI: 10.1007/s11253-012-0641-1