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Linear Groups with Almost Right Engel Elements
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 62 / Issue 3 / August 2019
- Published online by Cambridge University Press:
- 30 January 2019, pp. 789-797
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- Article
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Let G be a linear group such that for every g ∈ G there is a finite set
${\cal R}(g)$ with the property that for every x ∈ G all sufficiently long commutators [g, x, x, …, x] belong to 
${\cal R}(g)$. We prove that G is finite-by-hypercentral.
THE
$(2,3)$ -GENERATION OF THE SPECIAL LINEAR GROUPS OVER FINITE FIELDS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 95 / Issue 1 / February 2017
- Published online by Cambridge University Press:
- 26 September 2016, pp. 48-53
- Print publication:
- February 2017
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- Article
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We complete the classification of the finite special linear groups
$\text{SL}_{n}(q)$ which are 
$(2,3)$ -generated, that is, which are generated by an involution and an element of order 
$3$ . This also gives the classification of the finite simple groups 
$\text{PSL}_{n}(q)$ which are 
$(2,3)$ -generated.
