2-nilpotent multiplier and 2-capability of finite 2-generator p-groups of class two

TL;DR

This paper explicitly determines the structure of the 2-nilpotent multiplier for finite 2-generator p-groups of class two and characterizes which of these groups are 2-capable, advancing understanding of their algebraic properties.

Contribution

It provides an explicit description of the 2-nilpotent multiplier and characterizes 2-capable groups within this class, which was previously not fully understood.

Findings

Explicit structure of 2-nilpotent multiplier for these groups

Characterization of 2-capable groups in the class

Enhanced understanding of algebraic properties of 2-generator p-groups

Abstract

Let p be a prime number. We give the explicit structure of 2- nilpotent multiplier for each finite 2-generator p-group of class two. Moreover, 2-capable groups in that class are characterized.