The powerful class of groups

2023/10/03 by Moravec, Primoz
#20D15 #20E18 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2310.02073

Abstract

Pro-p groups of finite powerful class are studied. We prove that these are p-adic analytic, and further describe their structure when their powerful class is small. It is also shown that there are only finitely many finite p-groups of fixed coclass and powerful class.

Related

• Powerfully embedded subgroups of extensions of powerful pro-p groups
• Some Characterisations of p-adic Analytic Groups
• A characterization of powerful p-groups
• Quasi-powerful p-groups
• Powerfully nilpotent groups