Groups with a base property analogous to that of vector spaces

Paul Apisa; Benjamin Klopsch

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arXiv · 1211.6137

Groups with a base property analogous to that of vector spaces

Paul Apisa·Benjamin Klopsch

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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.

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Paul Apisa, Benjamin Klopsch. 2012-11-26. Groups with a base property analogous to that of vector spaces. https://arxiv.org/abs/1211.6137

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