On the Christensen-Wang bounds for the ghost number of a p-group algebra

TL;DR

This paper investigates bounds on the ghost number of p-group algebras, providing proofs for the upper bound and most cases of the lower bound using radical nilpotency results.

Contribution

It applies Koshitani and Motose's results to prove Christensen and Wang's conjectural bounds for the ghost number.

Findings

Proved the upper bound for the ghost number.

Established most cases of the lower bound.

Connected radical nilpotency index to ghost number bounds.

Abstract

Christensen and Wang give conjectural upper and lower bounds for the ghost number of the group algebra of a p-group. We apply results of Koshitani and Motose on the nilpotency index of the Jacobson radical to prove the upper bound and most cases of the lower bound.