منابع مشابه
groups 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 کاملTHE ORDER GRAPHS OF GROUPS
Let $G$ be a group. The order graph of $G$ is the (undirected)graph $Gamma(G)$,those whose vertices are non-trivial subgroups of $G$ and two distinctvertices $H$ and $K$ are adjacent if and only if either$o(H)|o(K)$ or $o(K)|o(H)$. In this paper, we investigate theinterplay between the group-theoretic properties of $G$ and thegraph-theoretic properties of $Gamma(G)$. For a finite group$G$, we s...
متن کاملExceptional Lie groups
Now, in the present book, we describe simply connected compact exceptional simple Lie groups G2, F4, E6, E7, E8, in very elementary way. The contents are given as follows. We first construct all simply connected compact exceptional Lie groups G concretely. Next, we find all involutive automorphisms σ of G, and determine the group structures of the fixed points subgroup G by σ. Note that they co...
متن کاملCharacterization of finite $p$-groups by the order of their Schur multipliers ($t(G)=7$)
Let $G$ be a finite $p$-group of order $p^n$ and $|{mathcal M}(G)|=p^{frac{1}{2}n(n-1)-t(G)}$, where ${mathcal M}(G)$ is the Schur multiplier of $G$ and $t(G)$ is a nonnegative integer. The classification of such groups $G$ is already known for $t(G)leq 6$. This paper extends the classification to $t(G)=7$.
متن کاملTHE STRUCTURE OF FINITE ABELIAN p-GROUPS BY THE ORDER OF THEIR SCHUR MULTIPLIERS
A well-known result of Green [4] shows for any finite p-group G of order p^n, there is an integer t(G) , say corank(G), such that |M(G)|=p^(1/2n(n-1)-t(G)) . Classifying all finite p-groups in terms of their corank, is still an open problem. In this paper we classify all finite abelian p-groups by their coranks.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2017
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2016.12.009