Changes

Jump to: navigation, search

Solvable not implies nilpotent

484 bytes added, 22:12, 18 June 2011
no edit summary
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.
|}
==Proof==
Bureaucrats, emailconfirmed, Administrators
38,756
edits

Navigation menu