Main Page

Welcome to Groupprops (The Group Properties Wiki). This is a pre-alpha stage group theory wiki primarily managed by Vipul Naik, a Ph.D. student in Mathematics at the University of Chicago. We have over 1000 articles including most material in basic group theory

Special introductions for: group theorists and teachers

Articles of the day:
<random>Permutable subgroup (DEFINITION): A subgroup that permutes with every other subgroup. May not be normal.@@@Hall subgroup (DEFINITION): A subgroup of a finite group whose order and index are relatively prime. Sylow subgroups are a special case.@@@Complete group (DEFINITION): A group whose center is trivial and for which every automorphism is inner.@@@Class-preserving automorphism: An automorphism of a group that sends every element to within its conjugacy class. May not be inner.@@@Baer norm (DEFINITION): The intersection of the normalizers of all subgroups of the group. Contains the center, and is a hereditarily normal subgroup.@@@Highly transitive group action (DEFINITION): A group action that is $k$-transitive for all natural numbers $k$.@@@Subnormal series: An ascending (resp., descending) series of subgroups with each subgroup normal in its successor (resp., predecessor).@@@Transitive subgroup property (DEFINITION): A subgroup satisfying the property inside a subgroup satisfying the property satisfies the property.</random>
The union of all conjugates of a proper subgroup in a finite group, can never be the whole group (FACT): And this breaks down for infinite groups
Nilpotent versus solvable (SURVEY ARTICLE): There are important differences between a nilpotent group and a solvable group

What we are: Eventually, a complete and reliable reference for group theory. For now, an exciting place to read definitions and facts of group theory, and navigate the relationships between them

What you can get: Quick access to definitions (learn more), facts (learn more), survey articles (learn more). An opportunity to explore relationships using the property-theoretic paradigm and the relational paradigm. Exciting add-ons like guided tours. The links in the left column will help you get around easily.

How to complement other resources: Complement with your group theory textbooks (learn more), use Wikipedia and Google Scholar more effectively. Enjoy the benefits of our searchbox.

What to watch out for: Read our conventions and beware of our hazards: none of the content here is peer-reviewed and very little has been verified by multiple sources.

How to join: Sign up and log in, and then proceed to customize your experience. Anybody can join, and you can learn more on contributing, if you're interested.

How to get help: Help:Contents can help with that. Also, use the request/feedback links in the left column.

What is Groupprops all about?: Read our purpose statement, and learn how we differ from Wikipedia

Are there more wikis like this?: Yes, there's The Differential Geometry Wiki, Topology Wiki, Commutative Algebra wiki and Noncommutative wiki