English

Finite soluble groups satisfying the replacement property

Group Theory 2017-10-31 v2

Abstract

We investigate the finite soluble groups GG with the following property (replacement property): for every irredundant generating set {g1,,gm}\{g_1,\dots,g_m\} of maximal size and for any 1gG1\neq g\in G there exists an i{1,,m}i\in \{1,\dots,m\} so that g1,,gi1,g,gi+1,,gm=G.\langle g_1,\dots,g_{i-1},g,g_{i+1},\dots,g_m\rangle=G.

Keywords

Cite

@article{arxiv.1710.00582,
  title  = {Finite soluble groups satisfying the replacement property},
  author = {A. Lucchini},
  journal= {arXiv preprint arXiv:1710.00582},
  year   = {2017}
}
R2 v1 2026-06-22T22:00:49.929Z