Classification of $p$-groups via their $2$-nilpotent multipliers

Peymam Niroomand; Mohsen Parvizi

doi:10.4171/rsmup/121

JournalsrsmupVol. 150pp. 127–136

Classification of $p$ -groups via their $2$ -nilpotent multipliers

Peymam Niroomand
Damghan University, Iran
Mohsen Parvizi
Ferdowsi University of Mashhad, Iran

Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

For a $p$ -group of order $p^{n}$ , it is known that the order of $2$ -nilpotent multiplier is equal to $∣ M^{(2)} (G)∣ = p^{\frac{1}{2} n (n - 1) (n - 2) + 3 - s_{2} (G)}$ , for an integer $s_{2} (G)$ . In this article, we characterize all non-abelian $p$ -groups satisfying $s_{2} (G) \in {1, 2, 3}$ .

Cite this article

Peymam Niroomand, Mohsen Parvizi, Classification of $p$ -groups via their $2$ -nilpotent multipliers. Rend. Sem. Mat. Univ. Padova 150 (2023), pp. 127–136

DOI 10.4171/RSMUP/121