Shahrood University of TechnologyJournal of Algebraic Systems2345-51286120180901ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS7180125610.22044/jas.2018.6328.1316ENZ. SepehrizadehDepartment of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran.
Email: zohreh.sepehri@gmail.comM. R. RismanchianDepartment of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran.
Email: rismanchian133@gmail.com, rismanchian@sku.ac.irJournal Article20171023In 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.http://jas.shahroodut.ac.ir/article_1256_9cb3d15cf6327aa4481ad9fb54223403.pdf