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Engel subgroups of triangular matrices over local rings. (English) Zbl 1099.20026

The authors describe, up to conjugacy, the maximal Engel subgroups of the full \(n\) by \(n\) upper triangular group over the local ring \(R\) with maximal ideal \(\mathbf m\), where either \(R\) is commutative or \(R\) is Artinian with \(R/\mathbf m\) commutative and \(\mathbf{m/m}^2\) central in \(R/{\mathbf m}^2\).

MSC:

20H25 Other matrix groups over rings
20F45 Engel conditions
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References:

[1] Shirvani, M.; Wehrfritz, B. A.F., Skew Linear Groups (1986), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0602.20046
[2] Sehgal, S. K., Topics in Group Rings (1978), Dekker: Dekker New York · Zbl 0411.16004
[3] Suprunenko, D. A., Matrix Groups, Transl. Math. Monogr., vol. 45 (1976), Amer. Math. Soc.: Amer. Math. Soc. Providence, RI · Zbl 0317.20028
[4] Wehrfritz, B. A.F., Infinite Linear Groups (1973), Springer-Verlag: Springer-Verlag New York · Zbl 0261.20038
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