BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Natalia Maslova (Russian Academy of Sciences) DTSTART:20210506T150000Z DTEND:20210506T160000Z DTSTAMP:20260423T021322Z UID:GOThIC/27 DESCRIPTION:Title: On pronormality of subgroups of odd index in finite groups\nby Natalia Maslova (Russian Academy of Sciences) as part of GOThIC - Ischia Online G roup Theory Conference\n\n\nAbstract\nIn this talk we discuss a recent pro gress in research of pronormality of subgroups of odd index in finite grou ps.\n\nA subgroup $H$ of a group $G$ is pronormal in $G$ if for any elemen t $g$ from $G$\, subgroups $H$ and $H^g$ are conjugate in the subgroup $\\ langle H\, H^g \\rangle$ generated by $H$ and $H^g$. Some problems in Fini te Group Theory\, Combinatorics\, and Permutation Group Theory were solved in terms of pronormality (see\, for example\, remarkable results by L. Ba bai\, P. Palfy\, Ch. Praeger\, and others). Thus\, the question of descrip tion of families of pronormal subgroups in finite groups is of interest. W ell-known examples of pronormal subgroups in finite groups are normal subg roups\, maximal subgroups\, Sylow subgroups\, Carter subgroups\, Hall subg roups of solvable groups\, and so on.\n\nIn 2012\, E.P. Vdovin and D.O. Re vin proved that the Hall subgroups are pronormal in finite simple groups a nd conjectured that the subgroups of odd index are pronormal in finite sim ple groups. This conjecture was disproved by A.S. Kondrat'ev\, the speaker \, and D. Revin in 2016. However\, in many finite simple groups the subgro ups of odd index are pronormal. Moreover\, the question of pronormality of a subgroup of odd index in an arbitrary finite group can be partially red uced to questions of pronormality of some subgroups of odd indices in its chief factors.\n\nThis talk is partially based on joint results with S. Gl asby\, A.S. Kondrat’ev\, C.E. Praeger\, and D.O. Revin.\n LOCATION:https://researchseminars.org/talk/GOThIC/27/ END:VEVENT END:VCALENDAR