## Introduction to Theory of Groups of Finite Order |

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Abelian group abstract group alternating group coefficients commutator subgroup complete set conjugate elements corollary corresponding cyclic group denote dicyclic group direct product distinct doubly transitive group element of order elements of G equation factor finite group following theorem form a group G and G G contains G of order GF[pn group G group of degree group of isomorphisms group of order Hamiltonian group Hence identity inner isomorphisms invariant irreducible isomorphism of G Let G Let H letters linear homogeneous transformations modulo multiplication non-Abelian group number of elements order pm ordered set permutation group PG(k positive integer prime number prime-power group proper subgroup replaces representation roots of unity self-conjugate in G self-conjugate subgroup set of conjugate set of elements Show simply isomorphic subgroup H subgroup of G subgroup of index subgroup of order Sylow subgroups symbols symmetric group tion variables whence it follows zero