2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59837Let $K$ be a field of characteristic $p$ and $G$ a nonabelian metacyclic finite $p$-group. We give an explicit list of all metacyclic $p$-groups $G$, such that the group algebra $KG$ over a field of characteristic $p$ has a filtered multiplicative $K$-basis. We also present an example of a non-metacyclic 2-group $G$, such that the group algebra $KG$ over any field of characteristic 2 has a filtered multiplicative $K$-basis.10 pages, AMS-TeXRings and AlgebrasRepresentation TheoryPrimary 1646A, 16A26, 20C05. Secondary 19A22text