2009/05/03 by Robert M. Guralnick, R. M. Guralnick, W. M. Kantor +9
Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory #graph theory and CDMA systems #math.GR
paper · pdf · doi:10.48550/arxiv.0905.0256
arxiv created 2009/05/03 · openalex publication_date 2009/05/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If a finite group G has a presentation with d generators and r relations, it is well-known that r - d is at least the rank of the Schur multiplier of G; a presentation is called efficient if equality holds. There is an analogous definition for proficient profinite presentations. We show that many perfect groups have proficient presentations. Moreover, we prove that infinitely many alternating groups, symmetric groups and their double covers have proficient presentations