Abstract
Assume \(p\) is a prime and \(G\) is a finite \(p\)-group. We prove that if \(G\) is a non-metabelian \({{\mathcal {A}}}_4\)-group, then \(p^{6}\leqslant |G|\leqslant p^{9}\). Moreover, if \(p\geqslant 5\), then \(p^{6}\leqslant |G|\leqslant p^{8}\).
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The author cordially thanks the referee for her/his detailed reading and valuable comments. Thanks also to Professor Qinhai Zhang for his helpful suggestions.
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Song, Q., Wang, Y. A note on non-metabelian \({{\mathcal {A}}}_4\)-groups. Ricerche mat (2023). https://doi.org/10.1007/s11587-022-00744-y
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DOI: https://doi.org/10.1007/s11587-022-00744-y
Keywords
- Finite \(p\)-groups
- Regular \(p\)-groups
- Metabelian groups
- \({{\mathcal {A}}}_t\)-groups
- Minimal nonabelian subgroups