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Conjugation diameter of the symmetric groups

Assaf Libman and Charlotte Tarry

Vol. 13 (2020), No. 4, 655–672

The conjugation diameter of a group G is the largest diameter of its Cayley graphs with respect to conjugation-invariant generating sets. It is a strong form of the extensively studied concept of the diameter of G. We compute the conjugation diameter of the symmetric groups.

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conjugation diameter, symmetric groups
Mathematical Subject Classification 2010
Primary: 05E15, 20B30
Received: 4 March 2020
Revised: 10 May 2020
Accepted: 25 June 2020
Published: 20 November 2020

Communicated by Kenneth S. Berenhaut
Assaf Libman
Institute of Mathematics
University of Aberdeen
King’s College
United Kingdom
Charlotte Tarry
Institute of Mathematics
University of Aberdeen
King’s College
United Kingdom