A non-abelian 2-group whose endomorphisms generate a ring, and other examples of E-groups
Groups for which the distributively generated near-ring generated by the endomorphisms is in fact a ring are known as E-groups and are discussed in (3). R. Faudree in (1) has given the only published examples of non-abelian E-groups by presenting defining relations for a family of p–groups. However, as shown in (3), Faudree's group does not have the desired property when p = 2.
E-groups Do Not Have Proper Semidirect Sum Decompositions
An E-group is a group in which each element commutes with any of its endomorphic images. Hence E-groups provide a generalization of abelian groups. It is easy to show that the endomorphism near-ring (the group generated additively by the endomorphisms) of an E-group is a ring, just as the endomorphism near-ring of an abelian group is a ring. In this paper, we establish the fact that, like abelian groups, E-groups have no proper semidirect sum decompositions (i.e. a semidirect sum decomposition of an E-group must be a direct sum decomposition).
Comparative studies of α-Lactalbumin and lysozyme: Echidna lysozyme
Summaryα-Lactalbumin is a modifier protein for galactosyl transferase in the biosynthesis of lactose and lysozyme catalyses the cleavage of β(1–4) glycosidic linkages. It is now generally believed that α-lactalbumin and lysozyme have diverged from a common ancestor. Comparative studies of these proteins from several species are reported here.The presence of lactose and lactose synthetase activity is shown in mature milk samples from a variety of placental mammals (eutheria) and a pouch bearing mammal (marsupialia). The isolation of the α-lactalbumins involved and their properties are compared.The position is different in the milk samples of monotremes. The α-lactalbumin, lactose and lactose synthetase activity levels in the two platypus samples studied are very low. The levels of lactose and lactose synthetase activity in some echidna(Tachyglossus aculeatus) samples are low, but appreciable in others. No α-lactalbumin is present. The lysozyme activity is appreciable, some samples containing a different lysozyme from that present in others. One of these (designated echidna lysozyme I) is capable of lactose synthetase modifier activity in the presence of bovine “A protein”.The properties of this lysozyme are compared with those of lysozymes and α-lactalbumins from a variety of species and their significance is discussed.