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    Groups and Subgroups

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    Let G be a group of order 2k , that contains a cyclic subgroup of order k, where k is odd.
    Determine a formula to compute the number of subgroups of G that are of odd order.

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    Solution Summary

    The solution to the above problem is given step by step using the relevant theorem.
    Students can understand easily this abstract computation of the number of odd subgroups in a given group and can work out similar problems using this model as an example.