Notes on Group Theory VII

In the first of these notes, the conditions have been discussed for a mapping {m} - i.e. the representation of each element a of a group G by a^m to be an endomorphism. Denoting by E(G) the set of numbers m for which {m} is an endomorphism and by M = M(G) the smallest positive number out of E(G) which maps G on an Abelian subgroup, say A(G), then the elements of E(G) were shown to form full classes of residues (mod M) satisfying certain conditions.