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Some Finite Groups with a Unique Proper Non-trivial Characteristic Subgroup

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Abstract

In this paper, first we give a necessary and sufficient condition on a non-abelian p-group G of exponent \(p^2\) \((p>2)\) possessing a unique proper non-trivial characteristic subgroup. Then we study some families of finite groups with a unique proper non-trivial characteristic subgroup. In particular, we study metacyclic groups, 2-generated p-groups, minimal non-abelian groups, \(A_2\)-group and also p-groups of order less than \(p^7\).

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Acknowledgements

The authors are grateful to the referee for his valuable suggestions. The paper was revised according to his comments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani Ave., Tehran, 1561836314, Iran

    Zeinab Kowsari, Shirin Fouladi & Reza Orfi

Authors
  1. Zeinab Kowsari
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  2. Shirin Fouladi
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  3. Reza Orfi
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Corresponding author

Correspondence to Shirin Fouladi.

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Communicated by Hamid Mousavi.

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Kowsari, Z., Fouladi, S. & Orfi, R. Some Finite Groups with a Unique Proper Non-trivial Characteristic Subgroup. Bull. Iran. Math. Soc. 48, 3457–3463 (2022). https://doi.org/10.1007/s41980-022-00705-z

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  • DOI: https://doi.org/10.1007/s41980-022-00705-z

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