Wehrfritz, B. A. F. Right Engel elements of stability groups of general series in vector spaces. (English) Zbl 1428.20036 Publ. Mat., Barc. 61, No. 1, 283-289 (2017). Summary: Let \(V\) be an arbitrary vector space over some division ring \(D\), \(\mathbf{L}\) a general series of subspaces of \(V\) covering all of \(V\;\{0\}\) and \(S\) the full stability subgroup of \(\mathbf{L}\) in \(\operatorname{GL}(V)\). We prove that always the set of bounded right Engel elements of \(S\) is equal to the \(\omega\)-th term of the upper central series of \(S\) and that the set of right Engel elements of \(S\) is frequently equal to the hypercentre of \(S\). MSC: 20F45 Engel conditions 20F19 Generalizations of solvable and nilpotent groups 20H25 Other matrix groups over rings Keywords:Engel elements; linear groups; stability groups × Cite Format Result Cite Review PDF Full Text: DOI Link