# A paper accepted by “Journal of the Australian Mathematical Society”

A new paper by **Evgeny Khukhro (Univ. of Lincoln), Pavel Shumyatsky (Univ. of Brasilia), and Gunnar Traustason (Univ. of Bath)** “Right Engel-type subgroups and length parameters of finite groups” has been accepted for publication in *Journal of the Australian Mathematical Society*. The results of this paper were partially obtained during Evgeny Khukhro’s research visit to University of Brasilia in July of 2018 (supported by a grant of CNPq-Brazil).

*Abstract*: Let be an element of a finite group and let be the subgroup generated by all the right Engel values over . In the case when is soluble we prove that if, for some , the Fitting height of is equal to , then belongs to the th Fitting subgroup . For nonsoluble , it is proved that if, for some , the generalized Fitting height of is equal to , then belongs to the generalized Fitting subgroup with depending only on and , where is the product of primes counting multiplicities. It is also proved that if, for some , the nonsoluble length of is equal to , then belongs to a normal subgroup whose nonsoluble length is bounded in terms of and . Earlier similar generalizations of Baer’s theorem (which states that an Engel element of a finite group belongs to the Fitting subgroup) were obtained by the first two authors in terms of left Engel-type subgroups.

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