Geodesic
On cohomologies and representations of groups with normal Engel subgroups
Eurasian mathematical journal, Tome 13 (2022) no. 2, pp. 70-81

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Let $\lambda$, $U$ be representations of a group $G$ with a normal Engel subgroup $N$. The paper studies triviality conditions for the cohomology group $\mathcal{H}^1(G,\lambda,U)$ when $\lambda$ and $U$ are sectionally spectrally disjoint and examines some decompositions of the extension $\mathfrak{e}(\lambda, U,\xi)$ of $\lambda$ by $U$ associated with non-trivial $(\lambda, U)$-cocycles $\xi$. 
@article{EMJ_2022_13_2_a6,
     author = {E. Kissin and V. S. Shulman},
     title = {On cohomologies and representations of groups with normal {Engel} subgroups},
     journal = {Eurasian mathematical journal},
     pages = {70--81},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2022_13_2_a6/}
}
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E. Kissin; V. S. Shulman. On cohomologies and representations of groups with normal Engel subgroups. Eurasian mathematical journal, Tome 13 (2022) no. 2, pp. 70-81. http://geodesic.mathdoc.fr/item/EMJ_2022_13_2_a6/