On Thompson's conjecture for alternating group of large degree

Ilya Gorshkov

On Thompson's conjecture for alternating group of large degree

Group Theory 2016-07-14 v1

Authors: Ilya Gorshkov

Abstract

For a finite group $G$ , let $N(G)$ denote the set of conjugacy class sizes of $G$ . We show that if every finite group $G$ with trivial center such that $N(G)$ equals to $N(Alt_n)$ , where $n>1361$ and at least one of numbers $n$ or $n-1$ are decomposed into a sum of two primes, then $G\simeq Alt_n$ .

Keywords

Thompson's conjecture alternating group finite group conjugacy class sizes trivial center

Cite

@article{arxiv.1607.03727,
  title  = {On Thompson's conjecture for alternating group of large degree},
  author = {Ilya Gorshkov},
  journal= {arXiv preprint arXiv:1607.03727},
  year   = {2016}
}

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