Small derived quotients in finite p-groups

2005/10/11 by Schneider, Csaba
#20-04 #20D15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0510223

Abstract

More than 70 years ago, P. Hall showed that if G is a finite p-group such that a term \der Gd+1 of the derived series is non-trivial, then the order of the quotient \der Gd/\der Gd+1 is at least p^2d+1. Recently Mann proved that, in a finite p-group, Hall's lower bound can be taken for at most two distinct d. We improve this result and show that if p is odd, then it can only be taken for two distinct d in a group with order p⁶.

Related

• The derived series of a finite p-group
• Groups of prime-power order with a small second derived quotient
• On exceptional groups of order p⁵
• On the regular power structure of p-groups and applications
• Classification of finite p-groups by the size of their Schur multipliers