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 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 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 کاملA Characterization of the Suzuki Groups by Order and the Largest Elements Order
One of the important problems in group theory is characterization of a group by a given property, that is, to prove there exist only one group with a given property. Let be a finite group. We denote by the largest order of elements of . In this paper, we prove that some Suzuki groups are characterizable by order and the largest order of elements. In fact, we prove that if is a group with an...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1918
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1918-1501093-5