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A note on groups whose non-normal subgroups are either abelian or minimal non-abelian

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Abstract

A group G is called parahamiltonian if each non-normal subgroup of G is either abelian or minimal non-abelian. Thus all biminimal non-abelian groups are parahamiltonian, and the class of parahamiltonian groups contains the important class of metahamiltonain groups, introduced by Romalis and Sesekin about 50 years ago. The aim of this paper is to describe the structure of locally graded parahamiltonian groups.

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Correspondence to Francesco de Giovanni.

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The second author is a member of GNSAGA (INdAM) and works within the ADV-AGTA project.

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Atlıhan, S., de Giovanni, F. A note on groups whose non-normal subgroups are either abelian or minimal non-abelian. Ricerche mat 67, 891–898 (2018). https://doi.org/10.1007/s11587-017-0344-x

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