Geodesic
On locally boundedly exactly doubly transitive lie groups of transformations of the space with a subgroup of parallel translations
Matematičeskie trudy, Tome 25 (2022) no. 2, pp. 126-148

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The paper solves the problem of extending the group of parallel translations of a three-dimensional space to a locally boundedly exactly doubly transitive group of transformations for the case of a decomposable Lie algebra. The Lie algebra of the required Lie group of transformations is represented as a semidirect sum of a commutative three-dimensional ideal and a three-dimensional Lie subalgebra. Basis operators are found for all Lie algebras of doubly transitive Lie groups of transformations with a subgroup of parallel translations. The Lie groups of transformations are restored from the basis operators. 
@article{MT_2022_25_2_a4,
     author = {V. A. Kyrov},
     title = {On locally boundedly exactly doubly transitive lie groups of transformations of the space with a subgroup of parallel translations},
     journal = {Matemati\v{c}eskie trudy},
     pages = {126--148},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2022_25_2_a4/}
}
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V. A. Kyrov. On locally boundedly exactly doubly transitive lie groups of transformations of the space with a subgroup of parallel translations. Matematičeskie trudy, Tome 25 (2022) no. 2, pp. 126-148. http://geodesic.mathdoc.fr/item/MT_2022_25_2_a4/