# Finite groups with the pp-embedding property

### Agnieszka Stocka

University of Białystok, Poland

## Abstract

A subset $X$ of a finite group $G$ is called g\nbdash independent if there is no proper subset $Y$ of $X$ such that $\langle Y,\Phi(G) \rangle = \langle X,\Phi(G) \rangle.$ The group $G$ has the embedding property if every g\nbdash independent subset of $G$ can be embedded in a minimal generating set of $G$.If $X$ is a set of prime power order elements, then we say that $G$ 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