Minimal partition-free groups
Group Theory
2020-10-21 v1
Abstract
Let G be a finite group. A collection P={H1, ..., Hr} of subgroups of G, where r > 1, is said a non-trivial partition of G if every non-identity element of G belongs to one and only one Hi, for some 1 <=i<=r. We call a group G that does not admit any non-trivial partition a partition-free group. In this paper, we study a partition-free group G whose all proper non-cyclic subgroups admit non-trivial partitions.
Keywords
Cite
@article{arxiv.2010.10476,
title = {Minimal partition-free groups},
author = {Afsane Bahri and Zeinab Akhlaghi and Behrooz Khosravi},
journal= {arXiv preprint arXiv:2010.10476},
year = {2020}
}