Show that the correspondence theorem preserves indices. More precisely, if a: G→G' is a surjective group homomorphism, and ker a CH C G and H'G' are sub- groups that correspond under the correspondence theorem, then |G: H| = |G' : H'|.
Show that the correspondence theorem preserves indices. More precisely, if a: G→G' is a surjective group homomorphism, and ker a CH C G and H'G' are sub- groups that correspond under the correspondence theorem, then |G: H| = |G' : H'|.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.5: Isomorphisms
Problem 7TFE: Label each of the following statements as either true or false. Two groups can be isomorphic even...
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