Abstract
Let G be the alternating group \({{\,\mathrm{Alt}\,}}(n)\) on n letters. We prove that for any \(\varepsilon > 0\), there exists \(N = N(\varepsilon ) \in \mathbb {N}\) such that whenever \(n \ge N\) and A, B, C, D are normal subsets of G each of size at least \(|G|^{1/2+\varepsilon }\), then \(ABCD = G\).
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Acknowledgements
The first author acknowledges the support of Fundação de Apoio à Pesquisa do Distrito Federal (FAPDF) - demanda espontânea 03/2016, and of Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) - Grant numbers 302134/2018-2, 422202/2018-5. The work of the second author on the project leading to this application has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 741420). He was also supported by the National Research, Development and Innovation Office (NKFIH) Grant no. K115799, Grant no. K132951, and Grant no. K135103
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Garonzi, M., Maróti, A. Alternating groups as products of four conjugacy classes. Arch. Math. 116, 121–130 (2021). https://doi.org/10.1007/s00013-020-01531-7
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DOI: https://doi.org/10.1007/s00013-020-01531-7