Problem 1. In each of the following, either prove or disprove that the given subset His a subgroup of G. 1.1. G = (Q,+) and H = { : a, d = Z with d\n}, where n € Z+ is fixed. 1.2. GS10, and H = {σ = S10 : |σ| = 4} U {e}. 1.3. G = GL2(R) and H = { ( a ) : a : a, b, c € R with ac 40}.

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 29E: Find the normalizer of the subgroup (1),(1,3)(2,4) of the octic group D4.
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Problem 1. In each of the following, either prove or disprove that the given subset
His a subgroup of G.
1.1. G = (Q,+) and H = { : a, d = Z with d\n}, where n € Z+ is fixed.
1.2. GS10, and H = {σ = S10 : |σ| = 4} U {e}.
1.3. G = GL2(R) and
H
=
{ ( a ) : a
: a, b, c € R with ac 40}.
Transcribed Image Text:Problem 1. In each of the following, either prove or disprove that the given subset His a subgroup of G. 1.1. G = (Q,+) and H = { : a, d = Z with d\n}, where n € Z+ is fixed. 1.2. GS10, and H = {σ = S10 : |σ| = 4} U {e}. 1.3. G = GL2(R) and H = { ( a ) : a : a, b, c € R with ac 40}.
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