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Solvable not implies nilpotent

484 bytes added, 22:12, 18 June 2011
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Not every [[solvable group]] is [[nilpotent group|nilpotent]].
==Definitions used==
{| class="sortable" border="1"
! Term !! Definition used
| [[nilpotent group]] || The [[upper central series]] terminates at the whole group. For a finite group, this is equivalent to being the [[direct product]] of its [[Sylow subgroup]]s (see [[finite nilpotent group]], [[equivalence of definitions of finite nilpotent group]]
| [[supersolvable group]] || There is a [[normal series]] where all the successive quotient groups are [[cyclic group]]s.
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