I know this should be obvious but somehow I can't seem to figure it out and it annoys me! My definition of nilpotent groups is the following: A group $G$ is nilpotent if every subgroup of $G$ is subnormal in $G$, or equivalently if $U
Nilpotent groups are solvable
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group-theory
solvable-groups
nilpotent-groups
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2You've marked this as "finite groups". Are you concerned *solely* with finite groups? Do you know that finite nilpotent groups are products of $p$-groups? – 2012-05-12
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0@ArturoMagidin: The given definition for *nilpotent* works only for finite groups (same for *solvable*). – 2012-05-13
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0@jug: Right; just like "product of $p$-groups" only works for finite groups. It should still be stated explicitly rather than implicitly, don't you think? – 2012-05-13