A Classification of Finite Metahamiltonian p-Groups
Xingui Fang , Lijian An
Communications in Mathematics and Statistics ›› 2021, Vol. 9 ›› Issue (2) : 239 -260.
A Classification of Finite Metahamiltonian p-Groups
A finite non-abelian group G is called metahamiltonian if every subgroup of G is either abelian or normal in G. If G is non-nilpotent, then the structure of G has been determined. If G is nilpotent, then the structure of G is determined by the structure of its Sylow subgroups. However, the classification of finite metahamiltonian p-groups is an unsolved problem. In this paper, finite metahamiltonian p-groups are completely classified up to isomorphism.
Minimal non-abelian groups / Hamiltonian groups / Metahamiltonian groups / ${\mathcal {A}}_2$-groups')">${\mathcal {A}}_2$-groups
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