(b) Let G = S5, H = ((123)), and (12345). List all elements of {ghg-1 | h E H}.

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 10E: 10. Suppose that and are subgroups of the abelian group such that . If is a subgroup of such...
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Abstract Algebra: Please do B

3.
Let G be a group, H a subgroup of G, and g and element of G.
(a) Prove that {ghg-1 | h e H} is always a subgroup of G.
(b) Let G = S5, H = ((123)), and g =
(12345). List all elements of {ghg- | h € H}.
Transcribed Image Text:3. Let G be a group, H a subgroup of G, and g and element of G. (a) Prove that {ghg-1 | h e H} is always a subgroup of G. (b) Let G = S5, H = ((123)), and g = (12345). List all elements of {ghg- | h € H}.
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