Suppose that (the commuting product of all components of ) is simple and contains a semisimple group involution. Then there is some semisimple group involution such that has a normal subgroup which is either quasisimple or isomorphic to and such that is tightly embedded.

# Aschbacher's Component Theorem

## See also

Group Involution, Isomorphic Groups, Normal Subgroup, Quasisimple Group, Simple Group, Tightly Embedded## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Aschbacher's Component Theorem." From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/AschbachersComponentTheorem.html