Algebras of p-Groups of Class 2 Over the Rationals

Abstract

In this work we analyze p-groups of class 2 G and H, with same rational group algebras. We prove that if QG = QH, then their commutators are equal and the centers, 𝒵(G) and 𝒵(H), have their orders preserved. We apply our results to Frattini Central p-groups, and we present an example of two groups of order p ⁷, with no isomorphic centers and different central cyclic components intersecting the cyclic components of the respective commutators groups.

Key Words:

• Frattini Central p-groups
• Group algebras
• Isomorphism of group algebras
• Representation Theory

2000 Mathematics Subject Classification:

• Primary 20C05, 20C15
• Secondary 20D15, 20D25

Notes

Communicated by S. Sehgal.