On prime-power groups in which the derived group has two generators

1957/01/01 by N. Blackburn, Norman Blackburn · 3 citations
Mathematics · #Rings, Modules, and Algebras #Finite Group Theory Research

paper · doi:10.1017/s0305004100031959

Abstract

Burnside ((1), p. 241) has proved the following theorem: If G is a non-metabelian p-group, then the centre of the derived group of G cannot be cyclic. In particular, a non-Abelian group of order p 3 cannot be the derived group of a p-group .

Cited by

• Index-\(p\) abelianization data of \(p\)-class tower groups
• Criteria for three-stage towers of p-class fields
• Finite p-groups all of whose subgroups of index p³ are abelian

Related

• The Generalized Burnside Theorem
• A straightforward solution to the Burnside Problem
• Commutators in finite p-groups with 3-generator derived subgroup
• A note on automorphisms of finite p-groups
• Commutators in finite p-groups with 2-generator derived subgroup