Geodesic
Finite groups whose all proper subgroups are $\mathcal {C}$-groups
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 513-522
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A group $G$ is said to be a $\mathcal {C}$-group if for every divisor $d$ of the order of $G$, there exists a subgroup $H$ of $G$ of order $d$ such that $H$ is normal or abnormal in $G$. We give a complete classification of those groups which are not $\mathcal {C}$-groups but all of whose proper subgroups are $\mathcal {C}$-groups.
A group $G$ is said to be a $\mathcal {C}$-group if for every divisor $d$ of the order of $G$, there exists a subgroup $H$ of $G$ of order $d$ such that $H$ is normal or abnormal in $G$. We give a complete classification of those groups which are not $\mathcal {C}$-groups but all of whose proper subgroups are $\mathcal {C}$-groups.
DOI : 10.21136/CMJ.2017.0542-16
Classification : 20D10, 20E34
Keywords: normal subgroup; abnormal subgroup; minimal non-$\mathcal {C}$-group 
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Guo, Pengfei; Liu, Jianjun. Finite groups whose all proper subgroups are $\mathcal {C}$-groups. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 513-522. doi: 10.21136/CMJ.2017.0542-16

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