منابع مشابه
On the Order of Primitive Groups
At the end of a memoir on primitive groups in the first volume of the Bulletin of the Mathematical Society of France, f Jordan announced the following theorem : Let q be a poaitive integer leas than 6, p any prime number greater than q; the degree of a primitive group G that contains a subatitutitm of order p on q cyclea (without including the alternating group) cannot exceed pq + q + 1. The pr...
متن کاملPrimitive coherent configurations: On the order of uniprimitive permutation groups
These notes describe the author’s elementary graph theoretic proof of the nearly tight exp(4 √ n ln n) bound on the order of primitive, not doubly transitive permutation groups (Ann. Math., 1981 ). The exposition incorporates a lemma by V. N. Zemlyachenko that simplifies the proof. The central concept in the proof is primitive coherent configurations, a combinatorial relaxation of the action of...
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 کاملPrime order derangements in primitive permutation groups
Let G be a transitive permutation group on a finite set Ω of size at least 2. An element of G is a derangement if it has no fixed points on Ω. Let r be a prime divisor of |Ω|. We say that G is r-elusive if it does not contain a derangement of order r, and strongly r-elusive if it does not contain one of r-power order. In this note we determine the r-elusive and strongly r-elusive primitive acti...
متن کاملon the order of the schur multiplier of a pair of finite $p$-groups ii
let $g$ be a finite $p$-group and $n$ be a normal subgroup of $g$ with $|n|=p^n$ and $|g/n|=p^m$. a result of ellis (1998) shows that the order of the schur multiplier of such a pair $(g,n)$ of finite $p$-groups is bounded by $ p^{frac{1}{2}n(2m+n-1)}$ and hence it is equal to $ p^{frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$. recently, the authors have characterized...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1915
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1915-1501006-3