Nilpotent Products of Cyclic Groups and Classification of p-Groups

Abstract

In 1940, Hall introduced the notion of isoclinism of groups for classifying all p-groups of order at most p ⁵(p > 3). According to this classification, all these groups are partitioned into ten families. This article intends to characterize all the families which have the nilpotent products of cyclic groups in themselves, and then determine the exact structures of these products.

Key Words:

• Classification of p-groups
• Nilpotent product of cyclic groups
• Isoclinism

2010 Mathematics Subject Classification:

• 20D15
• 20E99

Notes

Communicated by A. Olshanskii.