Answered: (a). ker() ◄ G. (b). H≤G⇒(H) ≤ y(G).… | bartleby

Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.3: Subgroups

Problem 12E: Prove or disprove that H={ hGh1=h } is a subgroup of the group G if G is abelian.

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11. Let : (G, *) → (G',') be a group homomorphism. Prove that
(a). ker() ◄ G.
(b). HAG⇒y(H) ≤ p(G).
(c). H'G'⇒¯¹(H') ≤G.
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