Groups of prime-power order with a small second derived quotient

2003/01/09 by Csaba Schneider, Schneider, Csaba
Computer Science · Mathematics · #20-04 #20D15 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GR #msc:20-04 #msc:20D15

paper · pdf · doi:10.48550/arxiv.math/0301078

16 pages

arxiv created 2003/01/09 · openalex publication_date 2003/01/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For odd primes we prove some structure theorems for finite p-groups G, such that G''≠ 1 and |G'/G''|=p³. Building on results of Blackburn and Hall, it is shown that \lcs G3 is a maximal subgroup of G', the group G has a central decomposition into two simpler subgroups, and, moreover, G' has one of two isomorphism types.

Citations

• On a special class of p-groups

Related

• On finite p-groups with powerful subgroups
• Small derived quotients in finite p-groups
• On the modular isomorphism problem for groups with center of index at most p³
• Groups having all elements off a normal subgroup with prime power order
• A note on automorphisms of finite p-groups