The book refers to augustus's government as "a monarchy disguised as a republic." what does this phrase mean? does this disguise continue throughout the empire period?

The phrase “a monarchy disguised as a republic” refers to Augustus’s government means that the people were promised to have the control over the government because the nation was Republic. However, the monarch family still empowered by their names and governs the country. This means that the nation is governed by the monarchy in disguised as a republic.

b: the establishment clause  

b: socialism