On Minimal Non-(residually Nilpotent) Locally Graded Groups
- Autores: A. O. Asar
- Localización: Mediterranean journal of mathematics, ISSN 1660-5446, Vol. 18, Nº. 2, 2021
- Idioma: inglés
- DOI: 10.1007/s00009-020-01664-7
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Resumen
In this work, characterizations of a locally graded periodic group whose proper subgroups are residually nilpotent are obtained. It is shown that if such a group is minimal non-(residually nilpotent), then, under certain conditions, it has a homomorphic image which is a barely transitive group. In particular a minimal non-hypercentral group whose proper subgroups are residually nilpotent has a barely transitive homomorphic image. As an application a related question about Heineken–Mohamed-type groups is answered. Finally, a short proof and a generalization of a result on the solvability of locally graded groups is given.
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