On a Theorem of Burnside.
In this paper we consider finite loops of specific order and we show that certain abelian groups are not isomorphic to inner mapping groups of these loops. By using our results we are able to construct a finite solvable group of order 120 which is not isomorphic to the multiplication group of a finite loop.
A group in a variety is said to be absolutely-, and we write , if central extensions by are again in . Absolutely-abelian groups have been classified by F. R. Beyl. In this paper we concentrate upon the class of absolutely-nilpotent of class groups. We prove some closure properties of the class and we show that every nilpotent of class group can be embedded in an -gvoup. We describe all metacyclic -groups and we characterize -generator and infinite -generator -groups. Finally...