Irreducible group

Main Question or Discussion Point

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?
 

Answers and Replies

morphism
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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?
 

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