On unit P-Groups in Group Algebra

Abstract:The aim of this paper we have define the group of units U(F(G)), where F(G) is the group algebra with G is finite group over a field F. Now if char F=0 and G nonabelian or F is a nonabsolute field of characterstic Pi 0 and G/ O Pi(G) is nonabelian, then it is well known that the group of unit U(K[G]) contains a nonabelain P-group.There for we will prove that there are two cyclic subgroups X and Y of G of prime power order and units uX in U(K[X]) and uY in U(K[X]) such that (uX,uY) contain nonabelian P-subgroups in linear group.