Groups whose non-normal subgroups are either nilpotent or minimal non-nilpotent
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913237871624192 |
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| author | Dastborhan, Nasrin Mousavi, Hamid |
| author_facet | Dastborhan, Nasrin Mousavi, Hamid |
| contents | Let $\mathfrak{Nil}$ be the class of nilpotent groups and $G$ be a group. We call $G$ a meta-$\mathfrak{Nil}$-Hamiltonian group if any of its non-$\mathfrak{Nil}$ subgroups is normal. Also, we call $G$ a para-$\mathfrak{Nil}$-Hamiltonian group if $G$ is a non-$\mathfrak{Nil}$ group and every non-normal subgroup of $G$ is either a $\mathfrak{Nil}$-group or a minimal non-$\mathfrak{Nil}$ group. In this paper we investigate the class of finitely generated meta-$\mathfrak{Nil}$-Hamiltonian and para-$\mathfrak{Nil}$-Hamiltonian groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00352 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Groups whose non-normal subgroups are either nilpotent or minimal non-nilpotent Dastborhan, Nasrin Mousavi, Hamid Group Theory 20D05, 20D99 Let $\mathfrak{Nil}$ be the class of nilpotent groups and $G$ be a group. We call $G$ a meta-$\mathfrak{Nil}$-Hamiltonian group if any of its non-$\mathfrak{Nil}$ subgroups is normal. Also, we call $G$ a para-$\mathfrak{Nil}$-Hamiltonian group if $G$ is a non-$\mathfrak{Nil}$ group and every non-normal subgroup of $G$ is either a $\mathfrak{Nil}$-group or a minimal non-$\mathfrak{Nil}$ group. In this paper we investigate the class of finitely generated meta-$\mathfrak{Nil}$-Hamiltonian and para-$\mathfrak{Nil}$-Hamiltonian groups. |
| title | Groups whose non-normal subgroups are either nilpotent or minimal non-nilpotent |
| topic | Group Theory 20D05, 20D99 |
| url | https://arxiv.org/abs/2311.00352 |