Primitive normal matrices and covering numbers of finite groups
نویسندگان
چکیده
منابع مشابه
Primitive normal matrices and covering numbers of nite groups
A primitive matrix is a square matrix M with nonnegative real entries such that the entries of M are all positive for some positive integer s. The smallest such s is called the primitivity index of M . Primitive matrices of normal type (namely: MM and MM have the same zero entries) occur naturally in studying the so called conjugacy-class covering numberand character covering numberof a ni...
متن کاملClassifying fuzzy normal subgroups of finite groups
In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.
متن کاملconjectures on the normal covering number of finite symmetric and alternating groups
let $gamma(s_n)$ be the minimum number of proper subgroups $h_i, i=1, dots, l $ of the symmetric group $s_n$ such that each element in $s_n$ lies in some conjugate of one of the $h_i.$ in this paper we conjecture that $$gamma(s_n)=frac{n}{2}left(1-frac{1}{p_1}right) left(1-frac{1}{p_2}right)+2,$$ where $p_1,p_2$ are the two smallest primes in the factorization of $ninmathbb{n}$ an...
متن کاملfactorization numbers of finite abelian groups
the number of factorizations of a finite abelian group as the product of two subgroups is computed in two different ways and a combinatorial identity involving gaussian binomial coefficients is presented.
متن کاملRelative non-Normal Graphs of a Subgroup of Finite Groups
Let G be a finite group and H,K be two subgroups of G. We introduce the relative non-normal graph of K with respect to H , denoted by NH,K, which is a bipartite graph with vertex sets HHK and KNK(H) and two vertices x ∈ H HK and y ∈ K NK(H) are adjacent if xy / ∈ H, where HK =Tk∈K Hk and NK(H) = {k ∈ K : Hk = H}. We determined some numerical invariants and state that when this graph is planar or...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2005
ISSN: 0024-3795
DOI: 10.1016/j.laa.2005.01.027