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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] G. M. Bergman, “Generating infinite symmetric groups”, Bull. London Math. Soc., 38 (2006), 429–440 | DOI | MR | Zbl

[2] J. D. Dixon, B. M. Mortimer, Permutation Groups, Graduate Texts in Mathematics, Springer, 1988

[3] F. Galvin, “Generating countable sets of permutations”, J. London Math. Soc. (2), 51 (1995), 230–242 | DOI | MR | Zbl

[4] H. Macpherson, P. M. Neumann, “Subgroups of Infinite Symmetric Groups”, J. London Math. Soc., 1990, 64–84 | DOI | Zbl

[5] G. Moran, “Conjugacy classes whose square is an infinite symmetric group”, Trans. Amer. Math. Soc., 316 (1989), 493–522 | DOI | MR | Zbl

[6] M. Droste, W. Ch. Holland, “Generating automorphism groups of chains”, Forum Mathematicum, 17:4 (2005), 699–710 | DOI | MR | Zbl

[7] M. Droste, “Classes of universal words for the infinite symmetric groups”, Algebra Universalis, 20 (1985), 205–216 | DOI | MR | Zbl

[8] M. Droste, R. Gobel, “Uncountable cofinalities of permutation groups”, J. London Math. Soc. (2), 71 (2005), 335–344 | DOI | MR | Zbl