Abstract
Let G be a finite group. A collection \(\Pi =\{H_1,\dots ,{H_r}\}\) 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 \(H_i\), for some \(1\leqslant i\leqslant r\). 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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The Zeinab Akhlaghi was in part supported by a Grant from IPM (No. 99200028)
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Bahri, A., Akhlaghi, Z. & Khosravi, B. Minimal partition-free groups. Ricerche mat 72, 753–770 (2023). https://doi.org/10.1007/s11587-021-00579-z
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DOI: https://doi.org/10.1007/s11587-021-00579-z