Nerve net Nerve net A nerve net consists of interconnected neurons lacking a brain or any form of cephalization. While organisms with bilateral body symmetry are normally associated with a central nervous system, organisms with radial symmetry are associated with nerve nets. Nerve nets can be found in members of the Cnidaria, Ctenophora, and Echinodermata phyla, all of which are found in marine environments. Nerve nets can provide animals with the ability to sense objects through the use of the sensory neurons within the nerve net. The nerve net is the simplest form of a nervous system found in multicellular organisms. Unlike
Subgroups of cyclic groups on no generators), this result can be seen as a special case of the Nielsen–Schreier theorem that every subgroup of a free group is itself free. The fundamental theorem for finite cyclic groups can be established from the same theorem for the infinite cyclic groups, by viewing each finite cyclic group as a quotient group of the infinite cyclic group. In both the finite and the infinite case, the lattice of subgroups of a cyclic group is isomorphic to the dual of a divisibility lattice. In the finite case, the lattice of subgroups of a cyclic group of order "n"