Study on Isomorphism of Finite Groups and It’s Impact (Journal of Advances and Scholarly Researches in Allied Education, 2023)
A present paper to analysed the “Study on isomorphism of finite groups and it’s impact.” The study has shown that G/N satisfy the hypothesis of the theorem. For a group G is finite and the Arbitrary prime is p, we define a characteristic subgroup S-p(G), which is a generalization of the F (Frattini) subgroup of G, as follows: S-p(G) is the intersection of all increasing subgroups M of G such that G has the general degree index of M is G and M are mixed and co-prime to p\ if there is no. such maximal subgroup then we set Sp(G) = G. We obtain some results which characterize solvable groups. Some properties of the subgroup Sp(G) are also obtained. A characteristic subgroup Sp(G) characterize, compare and quantify the effectiveness and complexity of invariants for group isomorphism. The center inner automorphism commutator subgroups and groups, solvable radicals, abelian radicals, derived series and π-radicals and fitting groups. A depends on the type of symmetry Derivative series with basis in lower/upper and central part of factorial series. We see dimension of finite group has one greater and indivisible factor of the direct dimension.