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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

Citations:

Zbl 0034.305
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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
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