On Minimal Non-(residually Nilpotent) Locally Graded Groups

Abstract

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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Acknowledgements

The author is very grateful to the referee for a careful reading of the manuscript and for some in valuable suggestiions.

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Correspondence to A. O. Asar.

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Asar, A.O. On Minimal Non-(residually Nilpotent) Locally Graded Groups. Mediterr. J. Math. 18, 54 (2021). https://doi.org/10.1007/s00009-020-01664-7

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Mathematics Subject Classification

  • 20E 25
  • 20E 26
  • 20F 19
  • 20F 50