Animal mesoderm forms by enterocoelic pouching, through invagination of the endoderm. The main deuterostome phyla are the Echinodermata and the Chordata. Echinoderms are exclusively marine and include starfish, sea urchins, and sea cucumbers. The chordates are dominated by the vertebrates (animals with backbones), which consist of fishes, amphibians, reptiles, birds, and mammals. The deuterostomes also include the Hemichordata (acorn worms). The Ecdysozoa are protostomes, named after their shared trait of ecdysis, growth by moulting. They include the largest animal phylum, the Arthropoda, which contains insects, spiders, crabs, and their kin. All of these have a body divided into repeating segments, typically
Subgroups of cyclic groups Subgroups of cyclic groups In abstract algebra, every subgroup of a cyclic group is cyclic. Moreover, for a finite cyclic group of order "n", every subgroup's order is a divisor of "n", and there is exactly one subgroup for each divisor. This result has been called the fundamental theorem of cyclic groups. For every finite group "G" of order "n", the following statements are equivalent: This statement is known by various names such as characterization by subgroups. (See also cyclic group for some characterization.) There exist finite groups other than cyclic groups with the property that all proper subgroups are