Groups and Their Graphs: Clarifications of Normal Subgroup Theorem and Test for Normal Subgroup Elements

On page 123 of “Gropus and Their Graphs” by Grossman and Magnus I struggled understanding Theorem 6 and the test it provides. The theorem read more clearly for me with the following substitution:

“the set K that contains all elements of G such that...” becomes

“the set K containing every element of the group G such that...”

The following paragraph that contained the test was easier for me to understand with the following substitution:

“If f maps all elements onto I...” becomes

“If f maps all elements of G onto I...”

Hope this helps! Any comments or questions?

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