Abstract
In this paper, we introduce the probability that a subgroup H of a finite group G can be normal in G, the subgroup normality degree of H in G, as the ratio of the number of all pairs \({(h, g)\in H\times G}\) such that \({h^g\in H}\) by |H||G|. We give some upper and lower bounds for this probability and obtain the upper bound \({\frac{8}{15}}\) for nontrivial subgroups of finite simple groups. In addition, we obtain explicit formulas for subgroup normality degrees of some particular classes of finite groups.
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Saeedi, F., Farrokhi D. G., M. & Jafari, S.H. Subgroup normality degrees of finite groups I. Arch. Math. 96, 215–224 (2011). https://doi.org/10.1007/s00013-011-0234-5
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DOI: https://doi.org/10.1007/s00013-011-0234-5