On Pronormal Subgroups in Finite Simple Groups. / Kondrat'ev, A. S.; Maslova, N. V.; Revin, D. O.
In: Doklady Mathematics, Vol. 98, No. 2, 01.09.2018, p. 405-408.Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - On Pronormal Subgroups in Finite Simple Groups
AU - Kondrat'ev, A. S.
AU - Maslova, N. V.
AU - Revin, D. O.
PY - 2018/9/1
Y1 - 2018/9/1
N2 - 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.
AB - 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.
KW - PRIMITIVE PERMUTATION-GROUPS
KW - ODD INDEX
UR - http://www.scopus.com/inward/record.url?scp=85053177315&partnerID=8YFLogxK
U2 - 10.1134/S1064562418060029
DO - 10.1134/S1064562418060029
M3 - Article
VL - 98
SP - 405
EP - 408
JO - Doklady Mathematics
JF - Doklady Mathematics
SN - 1064-5624
IS - 2
ER -
ID: 24444894