## Introduction to the Theory of Groups of Finite Order |

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Abelian group abstract group according alternating group belongs called characteristic coefficients common commutator conjugate consider consisting constitute Construct contains corresponding cyclic group defining relations denote Determine direct product distinct element of order elements of G equal equation exists fact factor field finite group fixed follows function G and H G contains G of order given greater group G group of degree group of order Hence homogeneous transformations identity independent invariant isomorphism of G least leaves Let G letters marks means modulo multiplication named obtained obvious permutation group prime primitive proof properties prove readily regular replaces representation represented respectively result roots satisfy self-conjugate subgroup Show shown simply isomorphic subgroup of G subgroup of order Sylow subgroups symbols symmetric group theorem tion transformations transitive group unity values variables whence zero