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.
2000 Mathematics Subject Classification:
Notes
Communicated by S. Sehgal.