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I want to ask for a hint or solution to this problem:

G acts faithfully on X, N is a minimal normal subgroup of G, N abelian, and acts transitively on X. Prove G acts primitively

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    Try pro$v$ing each of the following: (1) N acts regularly so WLOG N=X. (2) N has a complement H in G. (3) H acts irreducibly on N. (4) Anything bigger than H contains all of N.2012-04-12

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Show that normal subgroups preserve partitions.

Show that in this situation only the trivial partitions can be preserved.