All even permutations with large support are commutators of generating pairs

2014/03/11 by David Zmiaikou, Zmiaikou, David
Computer Science · Engineering · Mathematics · #Advanced Combinatorial Mathematics #Coding theory and cryptography #FOS: Mathematics #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1403.2775

openalex publication_date 2014/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish that any even permutation from A_n moving at least [3n/4] + o(n) points is the commutator of a generating pair of A_n and a generating pair of S_n. From this we deduce an exponential lower bound on the number of systems of transitivity in alternating and symmetric groups.

Related

• The probability of generating the symmetric group with a commutator condition
• Commutators of n-cycles in the symmetric group
• The Probability of Generating the Symmetric Group
• Permutations with Extremal number of Fixed Points
• A note on a question due to A. Garsia