2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141225Let p be a prime, K a field of characteristic p, G a locally finite p-group, KG the group algebra, and V the group of the units of KG with augmentation 1. The anti-automorphism g\mapsto g^{-1} of G extends linearly to KG; this extension leaves V setwise invariant, and its restriction to V followed by v\mapsto v^{-1} lives an automorphism of V. The elements of V fixed by this automorphism are called unitary; they form a subgroup. Our first theorem describes the K and G for which this subgroup is normal in V. For each element g in G, let \bar{g} denote the sum (in KG) of the distinct powers of g. The elements 1+(g-1)h\bar{g} with g,h\in G are the bicyclic units of KG. Our second theorem describes the K and G for which all bicyclic units are unitary.12 pagesRings and AlgebrasGroup Theory16U60; 16S34; 20C07text