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 -