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Dear All!

I tried for several evenings to find an answer to the following basic question and I cannot see what is the answer:

Given an integer $n\geq 3$, does there exist a an (infinite) group with exactly $n$ normal subgroups?

If "yes", what about the same questions for finitely generated groups, finitely presented groups?

I guess this must have been done.

1

# (F.g., f.p.) groups with exactly $n$ normal subgroups

Dear All!

I tried for several evenings to find an answer to the following basic question and I cannot see what is the answer:

Given an integer $n\geq 3$, does there exist a group with exactly $n$ normal subgroups?

If "yes", what about the same questions for finitely generated groups, finitely presented groups?

I guess this must have been done.