منابع مشابه
GROUPS 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 کاملOn 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 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 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 کاملAsymptotic Order of the Square-free Part of N!
The asymptotic order of the logarithm of the square-free part of n! is shown to be (log 2)n with error O( √ n).
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1976
ISSN: 0025-5718
DOI: 10.2307/2005332