Small derived quotients in finite p-groups
| dc.creator | Schneider, Csaba | |
| dc.date | 2005-10-11 | |
| dc.date | 2005-10-25 | |
| dc.date.accessioned | 2026-07-07T06:47:21Z | |
| dc.date.available | 2026-07-07T06:47:21Z | |
| dc.description | More than 70 years ago, P. Hall showed that if $G$ is a finite $p$-group such that a term $\der G{d+1}$ of the derived series is non-trivial, then the order of the quotient $\der Gd/\der G{d+1}$ is at least $p^{2^d+1}$. 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 $p^6$. | |
| dc.description | Two related papers have been submitted. The material have been reorganised for Versions 2 and results migrated between papers | |
| dc.identifier | https://arxiv.org/abs/math/0510223 | |
| dc.identifier | http://arxiv.org/abs/math/0510223 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103627 | |
| dc.subject | Group Theory | |
| dc.subject | 20D15, 20-04 | |
| dc.title | Small derived quotients in finite p-groups | |
| dc.type | text |