Geodesic
On generating sets of infinite symmetric group
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 37, Tome 500 (2021), pp. 177-187

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It was shown that in a group of bijections of an infinite set some families of subsets, related to the cardinality of some eigenspaces, are generating. Besides, we derived a criterion for generating by sets of this kind. 
@article{ZNSL_2021_500_a8,
     author = {A. V. Semenov and A. Denisova},
     title = {On generating sets of infinite symmetric group},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {177--187},
     publisher = {mathdoc},
     volume = {500},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_500_a8/}
}
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A. V. Semenov; A. Denisova. On generating sets of infinite symmetric group. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 37, Tome 500 (2021), pp. 177-187. http://geodesic.mathdoc.fr/item/ZNSL_2021_500_a8/