Abstract
Given a prime p and a subgroup A of a finite group G, we say that A is a p-CAP-subgroup of G if A covers or avoids every p-G-chief factor, where a p-G-chief factor is a G-chief factor of order divisible by p. We say that A is a strong p-CAP-subgroup of G if A is a p-CAP-subgroup of any subgroup of G containing A. We use the concept of strong p-CAP-subgroups to investigate the \(p\mathfrak{F}\)-hypercentrally embedded property of normal subgroups of a finite group and obtain some new results. Moreover, we extend the concept of (strong) p-CAP-subgroups to fusion systems and use this to characterize supersolvable and nilpotent fusion systems.
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The authors are grateful to the referee for a detailed and carefully written report, which led to improvements in the paper’s exposition.
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This work was supported by the National Natural Science Foundation of China (Grant No. 12301019).
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Gao, Y., Kaspczyk, J. Hypercyclically embedded property and supersolvable fusion systems. Czech Math J 76, 541–563 (2026). https://doi.org/10.21136/CMJ.2026.0330-25
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DOI: https://doi.org/10.21136/CMJ.2026.0330-25