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 €...

Abstract ALgebra: Please do A

Extracted 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}.