Groups with a base property analogous to that of vector spaces
Group Theory
2012-11-28 v1
Abstract
A B-group is a group such that all its minimal generating sets (with respect to inclusion) have the same size. We prove that the class of finite B-groups is closed under taking quotients and that every finite B-group is solvable. Via a complete classification of Frattini-free finite B-groups we obtain a general structure theorem for finite B-groups. Applications include new proofs for the characterization of finite matroid groups and the classification of finite groups with the basis property.
Cite
@article{arxiv.1211.6137,
title = {Groups with a base property analogous to that of vector spaces},
author = {Paul Apisa and Benjamin Klopsch},
journal= {arXiv preprint arXiv:1211.6137},
year = {2012}
}
Comments
10 pages