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(Law of Exponents for Abelian Groups) Let a and b be
Chapter 2, Problem 23E(choose chapter or problem)
QUESTION:
(Law of Exponents for Abelian Groups) Let a and b be elements of an Abelian group and let n be any integer. Show that (ab)n = anbn. Is this also true for non-Abelian groups?
Questions & Answers
QUESTION:
(Law of Exponents for Abelian Groups) Let a and b be elements of an Abelian group and let n be any integer. Show that (ab)n = anbn. Is this also true for non-Abelian groups?
ANSWER:Step 1 of 4
Let be an abelian group and are two elements of .
The Mathematical induction can be used to prove .
For ,
Here, is identity elements of .
For ,
Therefore, the statement is true of .