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Permutation Groups

See the attached file.
Modern Algebra
Group Theory (CXI)
Permutation Groups
Another Counting Principle

If O(G) = pn a prime number , prove that there exists subgroups Ni ( for some r) such that
G = N0 > N1 >N2 >N3 > ... >Nr = (e) where Ni is a normal subgroup of Ni-1 and where Ni-1 /Ni is abelian .
Here Ni-1>Ni means Ni-1 is superset of Ni.

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Modern Algebra
Group Theory (CXI)
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Solution Summary

This solution is comprised of a detailed explanation to prove that there exists subgroups Ni ( for some r) such that G = N0 > N1 >N2 >N3 > ... >Nr = (e) where Ni is a normal subgroup of Ni-1 and where Ni-1 /Ni is abelian.

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