Here are some words that use this root, with the stem "archy" often combined with other prefixes:
* Anarchy: Absence of government or control
* Monarchy: Rule by a single person, usually a king or queen
* Oligarchy: Rule by a small group of people
* Hierarchy: A system of ranking or organization
* Patriarchy: A social system where men hold power and authority
* Matriarchy: A social system where women hold power and authority
* Democracy: Rule by the people
* Technocracy: Rule by technical experts
* Theocracy: Rule by religious leaders
It's important to note that "archy" itself is not a stand-alone word but rather a part of a larger word.