mathmari
Gold Member
MHB
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Hey! 
I want to show that each group of order $135$ is nilpotent.
We have that $G$ is called nilpotent iff there is a series of normal subgroups $$1\leq N_1\leq N_2\leq \dots \leq N_k=G$$ such that $N_{i+1}/N_i\subseteq Z(G/N_i)\Leftrightarrow [G,N_{i+1}]\subseteq N_i$, right? (Wondering)
Could you maybe explain to me how we can find such a series? (Wondering)

I want to show that each group of order $135$ is nilpotent.
We have that $G$ is called nilpotent iff there is a series of normal subgroups $$1\leq N_1\leq N_2\leq \dots \leq N_k=G$$ such that $N_{i+1}/N_i\subseteq Z(G/N_i)\Leftrightarrow [G,N_{i+1}]\subseteq N_i$, right? (Wondering)
Could you maybe explain to me how we can find such a series? (Wondering)