Quotient group

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Let G be a group and let N be a normal subgroup of G. Then is the set of all cosets of N in G and is called the quotient group of N in G.

Simply, we can say that the quotient group of N in G as all elements in G that are not in N.[1]

This set is used in the proof of Lagrange's Theorem, for instance. In fact, the proof of Lagrange's theorem establishes that if

G is finite, then .

References[change | change source]

  1. "What's a Quotient Group, Really? Part 1". www.math3ma.com. Retrieved 2021-09-15.