2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145410Let V(KG) be a normalised unit group of the modular group algebra of a finite p-group G over the field K of p elements. We introduce a notion of symmetric subgroups in V(KG) as subgroups invariant under the action of the classical involution of the group algebra KG. We study properties of symmetric subgroups and construct a counterexample to the conjecture by V.Bovdi, which states that V(KG)=<G,S*>, where S* is a set of symmetric units of V(KG).5 pages, translated from original journal publication in RussianRings and AlgebrasGroup Theory16S34; 20C05text