The derived series of a finite p-group

2005/10/11 by Csaba Schneider, Schneider, Csaba
Mathematics · #20-04 #20D15 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR #msc:20-04 #msc:20D15

paper · pdf · doi:10.48550/arxiv.math/0510220

There are two related papers and version one had to be replaced after reogranisation of the material. Mathematical content is unchanged, but results have migrated from one paper to the other

openalex publication_date 2005/10/11 · arxiv created 2005/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite p-group, and let \der Gd denote the d-th term of the derived series of G. We show, for p≥ 5, that \der Gd≠ 1 implies log_p\ord G≥ 2^d+3d-6, and hence we improve a recent result by Mann.

Citations

• On a special class of p-groups

Related

• Small derived quotients in finite p-groups
• The derived series of GGS-groups
• On prime-power groups in which the derived group has two generators
• p-Groups with Derived Length Three and Three Character Degrees
• Abelianization of p-groups with derived subgroup of prime order