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Automorphisms of a finitary factor power of an infinite symmetric group

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We consider a semigroup \( FP_{\text{fin}}^{+} \left( {{\mathfrak{S}_{\text{fin}}}\left( \mathbb{N} \right)} \right) \) defined as a finitary factor power of a finitary symmetric group of countable order. It is proved that all automorphisms of \( FP_{\text{fin}}^{+} \left( {{\mathfrak{S}_{\text{fin}}}\left( \mathbb{N} \right)} \right) \) are induced by permutations from \( \mathfrak{S}\left( \mathbb{N} \right) \).

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References

  1. S. V. Hudzenko, “Green relation on factor powers of a symmetric group,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauk., No. 2, 24–44 (2004).

  2. A. G. Ganyushkin and V. S. Mazorchuk, “Factor powers and induced actions of the semigroups of transformations,” in: Abstr. of the Third Internat. Conf. on Algebra [in Russian], Krasnoyarsk (1993), pp. 83–84.

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Kyiv.

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 7, pp. 997–1001, July, 2010.

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S. V. Hudzenko. Automorphisms of a finitary factor power of an infinite symmetric group. Ukr Math J 62, 1158–1162 (2010). https://doi.org/10.1007/s11253-010-0420-9

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  • DOI: https://doi.org/10.1007/s11253-010-0420-9

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