Symmetry in biology Most radially symmetric animals are symmetrical about an axis extending from the center of the oral surface, which contains the mouth to the center of the opposite, , end. Radial symmetry is especially suitable for sessile animals such as the sea anemone, floating animals such as jellyfish, and slow moving organisms such as starfish. Animals in the phyla Cnidaria and Echinodermata are radially symmetric, although many sea anemones and some corals have bilateral symmetry defined by a single structure, the siphonoglyph. Many flowers are radially symmetric or actinomorphic. Roughly identical flower parts – petals, sepals, and stamens – occur at
Three subgroups lemma Three subgroups lemma In mathematics, more specifically group theory, the three subgroups lemma is a result concerning commutators. It is a consequence of the Philip Hall and Ernst Witt's eponymous identity. In that which follows, the following notation will be employed: Let "X", "Y" and "Z" be subgroups of a group "G", and assume Then formula_4. More generally, if formula_5, then if formula_6 and formula_7, then formula_8. Hall–Witt identity If formula_9, then Proof of the three subgroups lemma Let formula_11, formula_12, and formula_13. Then formula_14, and by the Hall–Witt identity above, it follows that formula_15 and so formula_16. Therefore, formula_17