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17.39 (2010)

Open

Is there a positive integer $n$ such that the hypercenter of any finite soluble group coincides with the intersection of $n$ system normalizers of that group? What is the least number with this property?

Contributor: A. F. Vasil’ev, L. A. Shemetkov

Progress

Comment of 2017: This is proved for groups with trivial Frattini subgroup (A. Ballester-Bolinches, J. Cossey, S. F. Kamornikov, H. Meng, J. Algebra, 499 (2018), 438–449).

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