Modern Algebra - #4

Let... Compute each of the following... Please see attached for full question.

Modern Algebra - #5

Let G be the real numbers under addition G' the positive real numbers under multiplication. Show that the mapping... is one to one and onto. Please see attached for the full question.

Modern Algebra - #7

Let G ---> H be a group homomorphism and... Show that if... then Φ[G] is albelian. Please see attached for full question.

Modern Algebra - #8

Let Φ be a homomorphism of group G into a group G'. Show that if e is the identity element of G, then Φ(e) is the identity element e' in G'.

Associative & Commutative Rule

Prove that addition modulo n, written +n is: 1) associative 2)comutative there are two ways to prove these properties. each way requires a definition or two: 1) for n≥2, 0≤a, b≤n+1 a+n(written as a power in a corner downside, but dont know how to put it tho) b={condition 1 - a+b if a+bor=n} 2) writing an(n is written as a power at the corner downside) for a mod n and (a+b)n(little n at the corner)=a+n(little n at the corner downside)b, then (p+nq)≡(Pn+qn)n (again n is written as a power at the corner but down the side not on the top) Do the proofs using both methods. which is more algebraic? I need you to go through the ... click for more