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math.GR2019
Engel elements in weakly branch groups
Gustavo A. Fernández-Alcober, Marialaura Noce, Gareth M. Tracey
We study properties of Engel elements in weakly branch groups, lying in the group of automorphisms of a spherically homogeneous rooted tree. More precisely, we prove that the set o…
math.GR2019★ 6 cited
On the generalized Fitting height and insoluble length of finite groups
Robert M. Guralnick, Gareth Tracey
We prove two conjectures of E. Khukhro and P. Shumyatsky concerning the Fitting height and insoluble length of finite groups. As a by-product of our methods, we also prove a genera…