منابع مشابه
A Simple Classification of Finite Groups of Order p2q2
Suppose G is a group of order p^2q^2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, respectively. In this paper, we show that up to isomorphism, there are four groups of order p^2q^2 when Q and P are cyclic, three groups when Q is a cyclic and P is an elementary ablian group, p^2+3p/2+7 groups when Q is an elementary ablian group an...
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 ...
متن کاملgroups of order $p^8$ and exponent $p$
we prove that for $p>7$ there are [ p^{4}+2p^{3}+20p^{2}+147p+(3p+29)gcd (p-1,3)+5gcd (p-1,4)+1246 ] groups of order $p^{8}$ with exponent $p$. if $p$ is a group of order $p^{8}$ and exponent $p$, and if $p$ has class $c>1$ then $p$ is a descendant of $p/gamma _{c}(p)$. for each group of exponent $p$ with order less than $p^{8} $ we calculate the number of descendants of o...
متن کاملSIMPLE p - ADIC GROUPS , II
0.1. For any finite group Γ, a “nonabelian Fourier transform matrix” was introduced in [L1]. This is a square matrix whose rows and columns are indexed by pairs formed by an element of Γ and an irreducible representation of the centralizer of that element (both defined up to conjugation). As shown in [L2], this matrix, which is unitary with square 1, enters (for suitable Γ) in the character for...
متن کاملClassification of finite simple groups whose Sylow 3-subgroups are of order 9
In this paper, without using the classification of finite simple groups, we determine the structure of finite simple groups whose Sylow 3-subgroups are of the order 9. More precisely, we classify finite simple groups whose Sylow 3-subgroups are elementary abelian of order 9.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1970
ISSN: 0021-8693
DOI: 10.1016/0021-8693(70)90023-2