Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771911 | Journal of Algebra | 2017 | 18 Pages |
Abstract
In 1974, Helmut Wielandt proved that in a finite group G, a subgroup A is subnormal if and only if it is subnormal in ãA,gã for all gâG. In this paper, we prove that the subnormality of an odd order nilpotent subgroup A of G is already guaranteed by a seemingly weaker condition: A is subnormal in G if for every conjugacy class C of G there exists câC for which A is subnormal in ãA,cã. We also prove the following property of finite non-abelian simple groups: if A is a subgroup of odd prime order p in a finite almost simple group G, then there exists a cyclic pâ²-subgroup of Fâ(G) which does not normalise any non-trivial p-subgroup of G that is generated by conjugates of A.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Francesco Fumagalli, Gunter Malle,