On solvable factors of almost simple groups

Burness，Timothy C.1; Li，Cai Heng2

2021-01-22

10.1016/j.aim.2020.107499

ADVANCES IN MATHEMATICS   影响因子和分区

0001-8708

1090-2082

Let G be a finite almost simple group with socle G. A (nontrivial) factorization of G is an expression of the form G=HK, where the factors H and K are core-free subgroups. There is an extensive literature on factorizations of almost simple groups, with important applications in permutation group theory and algebraic graph theory. In a recent paper, Xia and the second-named author describe the factorizations of almost simple groups with a solvable factor H. Several infinite families arise in the context of classical groups and in each case a solvable subgroup of G containing H∩G is identified. Building on this earlier work, in this paper we compute a sharp lower bound on the order of a solvable factor of every almost simple group and we determine the exact factorizations with a solvable factor. As an application, we describe the finite primitive permutation groups with a nilpotent regular subgroup, extending classical results of Burnside and Schur on cyclic regular subgroups, and more recent work of Li in the abelian case.

Almost simple groups Factorizations Primitive groups Regular subgroups

SCI

英语

其他

NSFC[11231008,11771200]

Mathematics

Mathematics

WOS:000601332900004

ACADEMIC PRESS INC ELSEVIER SCIENCE

MATHEMATICS

2-s2.0-85097238466

Scopus

1.School of Mathematics,University of Bristol,Bristol,BS8 1UG,United Kingdom
2.SUSTech International Center for Mathematics,Department of Mathematics,Southern University of Science and Technology,Shenzhen,518055,China

Burness，Timothy C.,Li，Cai Heng. On solvable factors of almost simple groups[J]. ADVANCES IN MATHEMATICS,2021,377.

Burness，Timothy C.,&Li，Cai Heng.(2021).On solvable factors of almost simple groups.ADVANCES IN MATHEMATICS,377.

Burness，Timothy C.,et al."On solvable factors of almost simple groups".ADVANCES IN MATHEMATICS 377(2021).