example of fully invariant subgroup

The derived subgroup [G,G] is a fully invariant subgroup because if f is an endomorphismMathworldPlanetmathPlanetmathPlanetmathPlanetmath of G, then for each word of commutatorsMathworldPlanetmath [a1,b1][a2,b2][am,bm], we have


i.e. the homomorphic imagePlanetmathPlanetmath of a word of commutators is a word of commutators.

Title example of fully invariant subgroup
Canonical name ExampleOfFullyInvariantSubgroup
Date of creation 2013-03-22 16:04:41
Last modified on 2013-03-22 16:04:41
Owner juanman (12619)
Last modified by juanman (12619)
Numerical id 5
Author juanman (12619)
Entry type Example
Classification msc 20D99
Related topic FullyInvariantSubgroup