At-groups with t + 1 generators

Abstract

We show that an ${\mathcal{A}}_t$-group which has exactly t + 1 generators is metahamiltonian, and such ${\mathcal{A}}_t$-groups are classified. This solved a problem proposed by Y. Berkovoch.

Keywords:

• ${\mathcal{A}}_t$-groups
• metahamiltonian groups
• extra-special p-groups

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D15

Acknowledgements

We owe our sincere gratitude to the referee. She/He read our paper very carefully and put forward a lot of suggestions. The author also thanks Professor Qinhai Zhang for his value suggestions. Their suggestions are quite valuable and helpful for improving our paper.

Additional information

Funding

This work was supported by NSFC(Nos.11771258, 11971280).