Nonprojectable Lie Group Actions and an Answer to Hilbert’s Fifth Problem

Abstract

It appears that, in the more recent literature, there is less than complete clarity or agreement about the original meaning of Hilbert’s fifth problem. This may not be so surprising, since the fifth problem happens to be one the few of those twenty three, formulated by Hilbert in 1900, which, although of a clear mathematical intent and content, nevertheless, has a certain rather inevitable vagueness or ambiguity, owing to the nature of the problem itself.