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If (G, *) is a group such that -1 (a ⋆ b)−¹ = a¯¹ ⋆ b−¹, for all a, b € G, then G is -1 * a/an Select one: O a. non-commutative semigroup O b. abelian group O c. non-abelian group O d. e. ring none of these

If (G, *) is a group such that -1 (a ⋆ b)−¹ = a¯¹ ⋆ b−¹, for all a, b € G, then G is -1 * a/an Select one: O a. non-commutative semigroup O b. abelian group O c. non-abelian group O d. e. ring none of these

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.8: Some Results On Finite Abelian Groups (optional)
Problem 6E: 6. For each of the following values of , describe all the abelian groups of order , up to...
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If (G, *) is a group such that (a ⋆ b)−¹ = a¯¹ ⋆ b−¹, for all a, b ≤ G, then G is * a/an Select one: O a. non-commutative semigroup b. abelian group c. non-abelian group O d. ring O e. none of these
Transcribed Image Text:If (G, *) is a group such that (a ⋆ b)−¹ = a¯¹ ⋆ b−¹, for all a, b ≤ G, then G is * a/an Select one: O a. non-commutative semigroup b. abelian group c. non-abelian group O d. ring O e. none of these
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