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Right Engel elements of stability groups of general series in vector spaces

B. A. F. Wehrfritz

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Let $V$ be an arbitrary vector space over some division ring $D$, $\mathbf{L}$ a general series of subspaces of $V$ covering all of $V\backslash \{0\}$ 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 $S$.

Article information

Publ. Mat., Volume 61, Number 1 (2017), 283-289.

Received: 27 August 2015
First available in Project Euclid: 22 December 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F45: Engel conditions 20F19: Generalizations of solvable and nilpotent groups 20H25: Other matrix groups over rings

Engel elements linear groups stability groups


Wehrfritz, B. A. F. Right Engel elements of stability groups of general series in vector spaces. Publ. Mat. 61 (2017), no. 1, 283--289. doi:10.5565/PUBLMAT_61117_11.

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