Finite groups with the pp-embedding property

  • Agnieszka Stocka

    University of Białystok, Poland
Finite groups with the pp-embedding property cover
Download PDF

A subscription is required to access this article.

Abstract

A subset XX of a finite group GG is called g\nbdash independent if there is no proper subset YY of XX such that Y,Φ(G)=X,Φ(G).\langle Y,\Phi(G) \rangle = \langle X,\Phi(G) \rangle. The group GG has the embedding property if every g\nbdash independent subset of GG can be embedded in a minimal generating set of GG.If XX is a set of prime power order elements, then we say that GG has the pp-embedding property. In this note we classify all finite solvable groups with the pp-embedding property. Moreover we prove that this class is equal to the class of finite solvable groups with the embedding property.

Cite this article

Agnieszka Stocka, Finite groups with the pp-embedding property. Rend. Sem. Mat. Univ. Padova 141 (2019), pp. 107–119

DOI 10.4171/RSMUP/16