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    Group Theory : Conjugacy, Cayley Table, Subgroups and Quotient Groups

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    Define the notion of conjugacy as it applies in a general group.
    Prove that the inverses of a pair of conjugate elements are also conjugate.
    Prove that conjugate elements have the same order. (6 marks)

    The remainder of this question concerns the group G , whose Cayley table is as

    [TABLE]
    (b) Determine the inverse and the order of each of the elements of G.

    (c) Simplify each of the following...

    (d) Given that the only element conjugate to g is g itself (you need not prove this), determine the conjugacy classes of G.

    (e) Find H , a normal subgroup of G having three elements. Identify the elements of the quotient group G/H , and determine its isomorphism type.

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    https://brainmass.com/math/group-theory/group-theory-conjugacy-cayley-table-subgroups-quotient-group-39332

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    Solution Summary

    Conjugacy, cayley table, subgroups and quotient groups are investigated and discussed. The solution is detailed and well presented.

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