  Let 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).
