Dmitruk, Yu. V. Sylow 2-subgroups of the countable alternating group. (English. Russian original) Zbl 0537.20001 Ukr. Math. J. 34, 291-294 (1983); translation from Ukr. Mat. Zh. 34, 356-360 (1982). We describe the structure of the Sylow 2-subgroups of the countable alternating group, i.e., the group of all even permutations of a countable set which move only finitely many points. The representation of Sylow p-subgroups of finite symmetric groups as polynomial tableaux introduced by L. Kaloujnine [Ann. Sci. Ec. Norm. Supér., III. Sér. 65, 239-276 (1948; Zbl 0034.305)] plays an important role in our description; it generalizes in a natural way to the case of countable permutation groups. MSC: 20B35 Subgroups of symmetric groups 20B07 General theory for infinite permutation groups 20E07 Subgroup theorems; subgroup growth Keywords:Sylow 2-subgroups; countable alternating group; Sylow p-subgroups of finite symmetric groups Citations:Zbl 0034.305 PDFBibTeX XMLCite \textit{Yu. V. Dmitruk}, Ukr. Math. J. 34, 291--294 (1983; Zbl 0537.20001); translation from Ukr. Mat. Zh. 34, 356--360 (1982) Full Text: DOI References: [1] I. D. Ivanyuta, ”Sylow p-subgroups of the countable symmetric group,” Ukr. Mat. Zh.,15, No. 3, 240–249 (1963). [2] Yu. V. Dmitruk and V. I. Sushchanskii, ”The structure of Sylow 2-subgroups of alternating groups and normalizers of Sylow subgroups in the symmetric and alternating groups,” Ukr. Mat. Zh.,33, No. 3, 304–312 (1971). · Zbl 0462.20003 [3] L. Kaloujnine, ”La structure des p-groupes de Sylow des groupes symetriques finis,” Ann. Sci. Ecole Norm. Super.,65, 239–276 (1948). · Zbl 0034.30501 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.