ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS | ||
| Journal of Algebraic Systems | ||
| مقاله 6، دوره 6، شماره 1، آذر 2018، صفحه 71-80 اصل مقاله (173.86 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2018.6328.1316 | ||
| نویسندگان | ||
| Z. Sepehrizadeh1؛ M. R. Rismanchian* 2 | ||
| 1Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: zohreh.sepehri@gmail.com | ||
| 2Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: rismanchian133@gmail.com, rismanchian@sku.ac.ir | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Autocommutativity degree؛ Characteristic degree؛ p-group | ||
|
آمار تعداد مشاهده مقاله: 513 تعداد دریافت فایل اصل مقاله: 462 |
||