Exercise 2.2. Let (G, *) be a group satisfying that (a* b)² = a² * 62 for every a, b = G. Show that G is abelian. Extended quesion* (Opt): What happens if the condition is replaced by (a + b)³ = a³ * 6³?
Exercise 2.2. Let (G, *) be a group satisfying that (a* b)² = a² * 62 for every a, b = G. Show that G is abelian. Extended quesion* (Opt): What happens if the condition is replaced by (a + b)³ = a³ * 6³?
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.6: Quotient Groups
Problem 31E: 31. (See Exercise 30.) Prove that if and are primes and is a nonabelian group of order , then the...
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