2 20. Let G be a group with subgroup H. Define a relation on G as follows: a b if b-¹a EH. Prove that this is an equivalence relation (that is, reflexive, symmetric, and transitive). Prove that a ~ b if and only if aH bH, and so the equivalence classes of this relation are the cosets in G/H. =
2 20. Let G be a group with subgroup H. Define a relation on G as follows: a b if b-¹a EH. Prove that this is an equivalence relation (that is, reflexive, symmetric, and transitive). Prove that a ~ b if and only if aH bH, and so the equivalence classes of this relation are the cosets in G/H. =
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 44E: 44. Let be a subgroup of a group .For, define the relation by
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