Characterization of Finite p-Groups by Their Non-Abelian Tensor Square

Abstract

Let G be a finite p-group of order p ⁿ with |G′| =p ^c and G ⊗ G be the non-abelian tensor square of G. In 1991, Rocco proved that |G ⊗ G| =p ^n(n−c)−l for some integer l ≥ 0. In this article we characterize all finite p-groups, for which |G′| =p and 0 ≤ l ≤ 10.

Key Words:

• Non-abelian tensor square
• Schur multiplier

2000 Mathematics Subject Classification:

• Primary 19C09
• Secondary 20D99

ACKNOWLEDGMENT

The authors thank the referee for many suggestions and corrections.

Notes

Communicated by A. Olshanskii.