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For an equation of fifth degree G will in general be of order 120 and will have a
normal subgroup of order 60, a simple group. In this situation Abel showed that
the equation could not be solved by radicals. direct products; abelian groups If
Further examples of natural transformations of functors can be given: (a) The
category "21 of Abelian groups and homomor- phisms is ... The torsion subgroup
A, of the Abelian group A consists of those elements of A that are of finite order.
... sequence is known and the limit term is related to an Abelian group to be
calculated, or, at least, about which information is sought. The relation of to this
group is frequently that of the graded group associated to a filtration of that group.
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