Chegg Guided Solutions for Modern Algebra An Introduction 6th Edition: Chapter 58

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  • Step 1 of 2

    We have a group of order 180. We need to find the orders of the Sylow p-subgroups of the group .

    We can factorize 180 as follows:

    From the above prime factorization we see that has Sylow 2-subgroup, Sylow 3-subgroup and Sylow 5-subgroup.

  • Step 2 of 2

    Now, the order of a Sylow p-subgroup is given by p raised to its highest power such that it divides the order of .

    Thus we have, the order of Sylow 2-subgroup as 4, Sylow 3-subgroup as 9 and Sylow 5-subgroup as 5.

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