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Exercise 7.20. A subgroup H of G is said to be maximal if it satisfies the following two properties: (1) H‡ G, and (2) If KG with HKCG, then K = G. Prove that the center of a group is never a maximal subgroup of a group.

Exercise 7.20. A subgroup H of G is said to be maximal if it satisfies the following two properties: (1) H‡ G, and (2) If KG with HKCG, then K = G. Prove that the center of a group is never a maximal subgroup of a group.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.7: Direct Sums (optional)
Problem 12E
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Exercise 7.20. A subgroup H of G is said to be maximal if it satisfies the following two properties: (1) H ‡ G, and (2) If KG with HÇ K ≤ G, then K = G. Prove that the center of a group is never a maximal subgroup of a group.
Transcribed Image Text:Exercise 7.20. A subgroup H of G is said to be maximal if it satisfies the following two properties: (1) H ‡ G, and (2) If KG with HÇ K ≤ G, then K = G. Prove that the center of a group is never a maximal subgroup of a group.
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