Matrotrophy associated with vertebrates and especially mammals, matrotrophy is found in 21 of 34 animal phyla, and is fairly common in 11 of those. It has arisen independently in more than 150 clades within Chordata and in more than 140 clades amongst invertebrates. Matrotrophy Matrotrophy is a form of maternal care during embryo development. Some flowering plants supplied the developing embryos for the first stages. The ovule has no stocks and the nutrients are provided by the "mother". In plants, matrotrophy is considered a critical evolutionary development preceding the origin of embryophytes and therefore essential to the evolution of land plants.
Klein four-group representation on four points: In this representation, V is a normal subgroup of the alternating group A (and also the symmetric group S) on four letters. In fact, it is the kernel of a surjective group homomorphism from S to S. Other representations within S are: They are not normal subgroups of S According to Galois theory, the existence of the Klein four-group (and in particular, the permutation representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals, as established by Lodovico Ferrari: the map corresponds to the resolvent cubic,