%0 Journal Article
%T ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Sepehrizadeh, Z.
%A Rismanchian, M. R.
%D 2018
%\ 09/01/2018
%V 6
%N 1
%P 71-80
%! ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS
%K Autocommutativity degree
%K Characteristic degree
%K p-group
%R 10.22044/jas.2018.6328.1316
%X In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic in G. We determine the upper and lower bounds for this probability. We also obtain a special lower bound, when H is a cyclic p-subgroup of G.
%U https://jas.shahroodut.ac.ir/article_1256_9cb3d15cf6327aa4481ad9fb54223403.pdf