Abstract
A p-group G is called a \(\mathcal {NCC}\)-p-group if \(N_G(\langle x\rangle )/\langle x\rangle \) is cyclic for every non-normal cyclic subgroup \(\langle x\rangle \) in G. In this paper, we give a complete classification of finite \(\mathcal {NCC}\)-p-groups.
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The research of the work is supported by “The Science & Technology Development Fund of Tianjin Education Commission for Higher Education (2019KJ141)” and “Tianjin Technical Expert Project under grant (21YDTPJC00120)”. The author would like to thank the referee for his or her valuable suggestions and useful comments which contributed to the final version of this paper.
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The research of the work was supported by “The Science & Technology Development Fund of Tianjin Education Commission for Higher Education(2019KJ141)” and “Tianjin Technical Expert Project under grant(21YDTPJC00120)”.
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Wang, J. Finite p-groups whose non-normal cyclic subgroups have cyclic quotient groups in their normalizers. Ricerche mat (2023). https://doi.org/10.1007/s11587-023-00797-7
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DOI: https://doi.org/10.1007/s11587-023-00797-7