What does irreducible mean for a cyclic subgroup of GL(n,F)?

[Hello Kitty]

What is the definition of an irreducible group. The context is that I have some theorem talking about "an irreducible cyclic subgroup of GL(n,F)". Is it one that can't be written as a product of two other subgroups in a non-trivial way?

 

[morphism]

A (semi)group of matrices is said to be irreducible if it has no nontrivial invariant subspaces. At least that's one definition of the word. Does it apply to your case?