Abstract
If \({\mathfrak {X}}\) is a class of groups, a group is minimal non-\({\mathfrak {X}}\) if it is not an \({\mathfrak {X}}\)-group, but all its proper subgroups belong to \({\mathfrak {X}}\). The aim of this paper is to prove that for a periodic locally graded group the property of being minimal non-(quasihamiltonian-by-finite) and that of being minimal non-(abelian-by-finite) are equivalent. Recall here that a group G is called quasihamiltonian if \(XY=YX\) for all subgroups X and Y of G.
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de Giovanni, F., Saccomanno, F. A note on groups whose proper subgroups are quasihamiltonian-by-finite. Ricerche mat 66, 619–627 (2017). https://doi.org/10.1007/s11587-017-0323-2
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DOI: https://doi.org/10.1007/s11587-017-0323-2