# Rendiconti del Seminario Matematico della Università di Padova

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**Published online first: 2018-11-20**

**DOI: 10.4171/RSMUP/16**

Finite groups with the pp-embedding property

Agnieszka Stocka^{[1]}(1) University of Białystok, Poland

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\nbdash embedding property. In this note we classify all finite solvable groups with the pp\nbdash embedding property. Moreover we prove that this class is equal to the class of finite solvable groups with the embedding property.

*Keywords: *Finite group, generating set, independent set, soluble group

Stocka Agnieszka: Finite groups with the pp-embedding property. *Rend. Sem. Mat. Univ. Padova* Electronically published on November 20, 2018. doi: 10.4171/RSMUP/16 (to appear in print)