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Finite groups whose all proper subgroups are $𝒞$ -groups

Pengfei Guo; Jianjun Liu — 2018

Czechoslovak Mathematical Journal

A group $G$ is said to be a $𝒞$ -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 $𝒞$ -groups but all of whose proper subgroups are $𝒞$ -groups.

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Finite groups whose all proper subgroups are 𝒞 -groups

Finite groups whose all proper subgroups are $𝒞$ -groups