# Groups and Subgroups

Question:

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.

https://brainmass.com/math/group-theory/groups-and-subgroups-163981

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Solution:

(The detailed step by step solution is given in the attached ...

#### 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.

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