Alternating groups as products of four conjugacy classes

Martino Garonzi; Attila Maróti

Alternating groups as products of four conjugacy classes

Group Theory 2020-06-16 v1

Authors: Martino Garonzi , Attila Maróti

Abstract

Let $G$ be the alternating group $\mbox{Alt}(n)$ on $n$ letters. We prove that for any $\varepsilon > 0$ there exists $N = N(\varepsilon) \in \mathbb{N}$ such that whenever $n \geq N$ and $A$ , $B$ , $C$ , $D$ are normal subsets of $G$ each of size at least $|G|^{1/2+\varepsilon}$ , then $ABCD = G$ .

Keywords

alternating groups conjugacy classes product of subsets normal subsets group theory

Cite

@article{arxiv.2006.07703,
  title  = {Alternating groups as products of four conjugacy classes},
  author = {Martino Garonzi and Attila Maróti},
  journal= {arXiv preprint arXiv:2006.07703},
  year   = {2020}
}

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