Let GGG be a group. A subnormal series is an ascending sequence of subgroups {e}=N0⊆N1⊆⋯⊆Nk−1⊆Nk=G\{e\} = N_0\subseteq N_1\subseteq \cdots\subseteq N_{k-1} \subseteq N_k = G{e}=N0⊆N1⊆⋯⊆Nk−1⊆Nk=G such that NiN_iNi is normal in Ni+1N_{i+1}Ni+1 for all 0≤i≤k0\leq i\leq k0≤i≤k.