Finite Two-Generator p-Groups with Cyclic Derived Group

Abstract

For an odd prime p, we classify the finite two-generator p-groups with cyclic derived group. There are eight types of non-isomorphic groups having at most nine parameters.

Key Words:

• Finite p-groups
• Regular p-groups
• Type invariants

AMS Subject Classification:

• 20D10
• 20D15

ACKNOWLEDGMENTS

The author is grateful to the referee. He pointed out some mistakes in the manuscript and checked the number of groups in Theorems 3.2 and 3.3 for the p-groups of order p ⁿ , where p = 3, 5, 7 and n ≤ 10. Furthermore, he offered assistance on the exposition and language of the article.

Thanks to Professor Don Taylor for his careful reading and helpful comments. These helped me to improve the article.

This work was supported by the National Natural Science Foundation of China (Grant No. 11071150), by NSF of Shanxi Province (No. 2008012001), by the Returned Abroad-student Fund of Shanxi province (No. [2011]8-059) and Young Scientist Fund (No. 11101252).

Notes

Communicated by A. Turull.