Group Theory (by Abstract Algebra) Exercise 14 solution pdf Exercise 14 👉Normal Subgroup 👉 Quotient group Normal subgroup: We absorve that when G=(Z,+) and H=(3Z,+) and, H=(3Z,+), each left coset of H is also a right coset of H ; when G=S3 and H={po,p1,p2), each left coset of H is also a right coset of H . But when G=S3 and H={po,p3}, H is a left coset as well as a right coset and other left cosets are not right cosets . Thus we see that for some subgroup the left cosets and and the right cosets and right cosets differ. Defination.Normal subgroup: A subgroup H of a group G is said to be a normal subgroup of G if Ha=aH holds for all a in G. The standard notation for "H is a normal subgroup of G ,is H∆G. Note 1. The condition aH = Ha does not demand that for every h €H, ah=ha. Note 2. When H is a...
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