TY - JOUR ID - 1256 TI - ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Sepehrizadeh, Z. AU - Rismanchian, M. R. AD - Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: zohreh.sepehri@gmail.com AD - Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: rismanchian133@gmail.com, rismanchian@sku.ac.ir Y1 - 2018 PY - 2018 VL - 6 IS - 1 SP - 71 EP - 80 KW - Autocommutativity degree KW - Characteristic degree KW - p-group DO - 10.22044/jas.2018.6328.1316 N2 - 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. UR - https://jas.shahroodut.ac.ir/article_1256.html L1 - https://jas.shahroodut.ac.ir/article_1256_9cb3d15cf6327aa4481ad9fb54223403.pdf ER -