What is it about?
Our result states that: if p is a prime number, then the groups Symp are determined up to isomorphism by their order and a special conjugacy class size of (p - 1)!.
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Why is it important?
By our result, we can conclude that Thompson's conjecture is valid under a weak condition for the symmetric groups of prime degree.
Perspectives
Is it true this result for the symmetric groups of degree n.
Alireza Khalili
Farhangian University, Tehran, Iran
Read the Original
This page is a summary of: New characterization of symmetric groups of prime degree, Acta Universitatis Sapientiae Mathematica, January 2017, De Gruyter,
DOI: 10.1515/ausm-2017-0001.
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