Minimal partition-free groups

Afsane Bahri; Zeinab Akhlaghi; Behrooz Khosravi

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arXiv · 2010.10476

Minimal partition-free groups

Afsane Bahri·Zeinab Akhlaghi·Behrooz Khosravi

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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.

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Afsane Bahri, Zeinab Akhlaghi, Behrooz Khosravi. 2020-10-20. Minimal partition-free groups. https://arxiv.org/abs/2010.10476

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