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    Group Theory : Cayley Tables, Cyclic Groups and Isomorphisms

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    ? I have the following cayley tables (which is in modulo 9)

    determine the order of each element . Prove that G is a cyclic group.

    ? Let be the symmetric group of degree 3 together with composition of maps. Is G isomorphic to ? Justify your answer.

    ? Let p be a prime number and G a group of order with identity element e. let and be a subgroup of G. prove that U is cyclic.

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    https://brainmass.com/math/group-theory/group-theory-cayley-tables-cyclic-groups-isomorphisms-31559

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    • I have the following cayley tables (which is in modulo 9)

    determine the order of each element . Prove that G is a cyclic group.

    • Let be the symmetric group of degree 3 together with composition of maps. Is G isomorphic to ? Justify your answer.

    • Let p be a prime number and G a group of order with identity element e. let and be a subgroup of G. prove that U is cyclic.

    Solution:
    1) We denote <a> the cyclic (sub)group generated by element (a), we ...

    Solution Summary

    Cayley Tables, Cyclic Groups and Isomorphisms are investigated.

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