I am reading the proof of Proposition 5 in Section 3.1 of Dummit and Foote's Abstract Algebra. Can someone please help me understand why $ng^{-1}\cdot 1\in ng^{-1}N$ implies $ng^{-1}\in g^{-1}N$?
2026-04-01 00:30:03.1775003403
Understanding an elementary proof from Dummit and Foote's Abstract Algebra
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In the previous line you showed $g^{-1} N = n g^{-1} N$.