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Prove that if N is a subgroup of G, and the operation (Na)(Nb) = N(ab) is well defined
Chapter 22, Problem 22.15(choose chapter or problem)
QUESTION:
Prove that if N is a subgroup of G, and the operation (Na)(Nb) = N(ab) is well defined onthe set G / N of all right cosets of N in G, then N
Questions & Answers
QUESTION:
Prove that if N is a subgroup of G, and the operation (Na)(Nb) = N(ab) is well defined onthe set G / N of all right cosets of N in G, then N
ANSWER:Step 1 of 2
Let us considerbe a group,be a subgroup of the group.
The well-defined operation is:
for all
Suppose that is the set of all right cosets ofis.
To show thatis a normal subgroup of, claim thatforand.
Consider a closet if: