On Pronormal Subgroups in Finite Simple Groups

A. S. Kondrat'ev, N. V. Maslova, D. O. Revin

Результат исследования: Научные публикации в периодических изданияхстатья

2 Цитирования (Scopus)

Аннотация

A subgroup H of a group G is called pronormal if, for any element g of G, the subgroups H and H-g are conjugate in the subgroup they generate. Some problems in the theory of permutation groups and combinatorics have been solved in terms of pronormality, and the characterization of pronormal subgroups in finite groups is a problem of importance for applications of group theory. A task of special interest is the study of pronormal subgroups in finite simple groups and direct products of such groups. In 2012 E.P. Vdovin and D.O. Revin conjectured that the subgroups of odd index in all finite simple groups are pronormal. We disproved this conjecture in 2016. Accordingly, a natural task is to classify finite simple groups in which the subgroups of odd index are pronormal. This paper completes the description of finite simple groups whose Sylow 2-subgroups contain their centralizers in the group and the subgroups of odd index in which are pronormal.

Язык оригиналаанглийский
Страницы (с-по)405-408
Число страниц4
ЖурналDoklady Mathematics
Том98
Номер выпуска2
DOI
СостояниеОпубликовано - 1 сен 2018
Опубликовано для внешнего пользованияДа

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