Otto H. Kegel’s Beautiful Contributions to Sylow Theory in Locally Finite Groups
DOI:
https://doi.org/10.47363/JMCA/2025(4)223Keywords:
locally finite group, p-uniqueness subgroup, finite p-subgroup singular in some locally finite group, (smooth simple straight) split sequence of finite p-perfect subgroups with its associated ascending sequence of subgroups, Sylow-separated (ascending) sequence of p-subgroups with its associated sequence of Sylow p-subgroups, (proper) Sylow p-intersection, p-blank of G in H, AGTA-Journal, Archiv der MathematikAbstract
Otto H. Kegel published two fundamental papers on Sylow Theory in locally finite groups: see [5] and [6]. The paper at hand summarises them, compares them and above all provides a list of their open issues which are still open until the present day. To study crucial configurations, Kegel developed in [6] the quite excogitated concept of the “(smooth simple straight) split sequences of finite p-perfect subgroups with their associated ascending sequences of subgroups ” which is related to his equally very fine concept of the “Sylow-separated (ascending) sequences of p-subgroups with associated sequences of Sylow p-subgroups ” he had developed already more then ten years earlier in [5]. When I met him personally in July 2022, I tried to find out how he detected these really ingenious ideas, but woefully was unsuccessful, although I was really very privileged to witness up very close the creation of the idea of [6] (see [3]). A scheduled new attempt in July 2025 (see [3]) could not be realised …. Mathematics Subject Classification (2020): 20D20, 20F50, 20D15, 20D06, 20D10