Lie principle

This survey article is about a correspondence-principle between: Lie group and finite group

The Lie principle is a general principle which states that there is a close parallel between the study of a finite group of Lie type in characteristic $p$ and an arbitrary finite group with respect to a prime $p$. The principle was enunciated by Jonathan L. Alperin in his survey article A Lie approach to finite groups, where he stated it as follows:

If $G$ is an arbitrary finite group and $p$ is any prime divisor of its order, then there exist interesting and important analogs of all aspects of the structure of Lie type groups whose natural characteristic is $p$

References

• A Lie approach to finite groups by Jonathan L. Alperin, Groups -- Canberra 1989, Lecture Notes in Mathematics Volume 1456, Pages 1-9; presented in Canberra 1989