groups n subroupsWatch

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#1
Determin with justification whether or not the given sets H1, H2 are subgroups of the given group G:

(i) G=R under addition, H1={x in R:x>=0}, H2=Z

(ii) G = S(R), H1= {f in G : f(2)=2}, H2= {f in G:f(2)=0}

S(R) meaning the set of bijections R---->R under composition.
0
14 years ago
#2
i) H1, no, theres no inverse. H2, yes
ii) H1 yes, H2 no, consider the composition of any two f, you must have some f such that f(0) = 0 and f(2) = 0, so it isnt a bijection.
0
14 years ago
#3
Maybe you should talk to Superkillball - you're clearly being set the same problem sheets.
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