On recognition by prime graph of the projective special linear group over GF(3)
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 $G/Nequiv G_2(5)$.
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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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As an infinite family of simple groups, the two dimensional special projective linear groups PSL(2,p) are interesting algebraic objects. While the groups are well known in the sense that their subgroup lattice structure is completely determined, properties of their generating sequences are still not entirely understood. With recent developments in this direction, one can begin to completely ans...
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چکیده ندارد.
15 صفحه اولCharacterizations of the simple group $D_{n}(3)$ by prime graph and spectrum
We prove that $D_n(3)$, where $ngeq6$ is even, is uniquely determined by its prime graph. Also, if $G$ is a finite group with the same prime graph as $D_4(3)$, then $Gcong D_4(3), B_3(3), C_3(3)$ or $G/O_2(G)cong {rm Aut}({}^2B_2(8))$.
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ژورنال
عنوان ژورنال: Publications de l'Institut Mathematique
سال: 2014
ISSN: 0350-1302,1820-7405
DOI: 10.2298/pim1409255k