Document Type : Original Manuscript

Authors

1 Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: zohreh.sepehri@gmail.com

2 Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: rismanchian133@gmail.com, rismanchian@sku.ac.ir

Abstract

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.

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