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1 a) Suppose G is a group and H is a subset of G. What must hold for H to be a subgroup of G? In other words, give the definition of a subgroup of a group G. b) Consider the subset S of integers defined as S = {…,−25,−15,−5,5,15,25,…} = {10r + 5 : r ∈ Z}. Is S a subgroup of (Z,+)? If so, explain why. If not, use the definition of subgroups to explain why not.

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a) Suppose G is a group and H is a subset of G. What must hold for H to be a subgroup of G? In other words, give the definition of a subgroup of a group G.

b)  Consider the subset S of integers defined as S = {…,−25,−15,−5,5,15,25,…} = {10r + 5 : r ∈ Z}. Is S a subgroup of (Z,+)? If so, explain why. If not, use the definition of subgroups to explain why not.

 
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