The p-width of the alternating groups

2017/10/13 by Alexander Malcolm, Alexander J. Malcolm, Malcolm, Alexander J.
Computer Science · Engineering · Mathematics · #20d06 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR #msc:20d06

paper · pdf · doi:10.48550/arxiv.1710.04972

Added Appendix concerning the work of Dvir85 that can be used to simplify the proof of our main theorem

openalex publication_date 2017/10/13 · arxiv created 2017/12/08 · arxiv updated 2017/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a fixed prime. For a finite group generated by elements of order p, the p-width is defined to be the minimal k∈ℕ such that any group element can be written as a product of at most k elements of order p. Let A_n denote the alternating group of even permutations on n letters. We show that the p-width of A_n (n≥ p) is at most 3. This result is sharp, as there are families of alternating groups with p-width precisely 3, for each prime p.

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• On the maximal number of elements pairwise generating the finite alternating group
• On the widths of finite groups (I)