Lie principle

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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 adn 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, in Groups -- Canberra 1989, Lecture Notes in Mathematics Volume 1456, Pages 1-9