15. Find groups H and K such that the following conditions are satisfied: a. H is a normal subgroup of K. b. K is a normal subgroup of the octic group. c. H is not a normal subgroup of the octic group.

15. Find groups H and K such that the following conditions are satisfied: a. H is a normal subgroup of K. b. K is a normal subgroup of the octic group. c. H is not a normal subgroup of the octic group.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 15E: Find groups H and K such that the following conditions are satisfied: H is a normal subgroup of K. K...

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Question

15. Find groups H and K such that the following conditions are satisfied:
a. H is a normal subgroup of K.
b. K is a normal subgroup of the octic group.
c. H is not a normal subgroup of the octic group.

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