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
Subnormal series: An ascending (resp., descending) series of subgroups with each subgroup normal in its successor (resp., predecessor).
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 get help: Help:Contents can help with that. Also, use the request/feedback links in the left column.