منابع مشابه
On automorphism groups of circulant digraphs of square-free order
We show that the full automorphism group of a circulant digraph of square-free order is either the intersection of two 2-closed groups, each of which is the wreath product of 2-closed groups of smaller degree, or contains a transitive normal subgroup which is the direct product of two 2-closed groups of smaller degree. The work in this paper makes contributions to the solutions of two problems ...
متن کاملGROUPS OF SQUARE - FREE ORDER , AN ALGORITHM 633 Definition
An abstract definition of the groups of square-free order is given that leads naturally to a programmable computation of their number. O. Holder's alternative description of the groups of square-free order is incidentally derived. Throughout this paper G will be a group of order h = n^j p;, where Pj > p2 > • • • >p„ are given prime numbers. 0. Holder proved in 1895 that the number of groups of ...
متن کاملSquare free values of the order function
Given a ∈ Z \ {±1, 0}, we consider the problem of enumerating the integers m coprime to a such that the order of a modulo m is square free. This question is raised in analogy to a result recently proved jointly with F. Saidak and I. Shparlinski where square free values of the Carmichael function are studied. The technique is the one of Hooley that uses the Chebotarev Density Theorem to enumerat...
متن کاملSquare-free graphs are multiplicative
Graph homomorphism is an ubiquitous notion in graph theory with a variety of applications, and a first step to understanding more general constraints given by relational structures, see e.g. the monograph of Hell and Nešetřil [5]. We write μ : G→ H if μ is a homomorphism from the graph G to H, or simply G → H if such a homomorphism exists. For example, a graph G is k-colorable iff it has a homo...
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: Pacific Journal of Mathematics
سال: 1980
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1980.91.373