Isomorphism
Note: ~~ means an isomorphism exists. Moreover,if an isomorphism existed from G to G1 I would say G ~~ G1
Questions: If G is an infinite cyclic group, show that G ~~ Z (Z is the set of integers)
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Proof:
G is an infinite cyclic group, then G=<a>, where a is a generator of G. Now we can define a map f from G to Z as follows:
for any b in G, b=a^i ...
Solution Summary
This is a proof regarding isomorphisms and infinite cyclic groups.
Let G be any group, g a fixed element in G. Define phi:G--> G by phi(x) = gxg^-1. Prove that phi is an isomorphism of G onto G.
Group theory
Modern Algebra
Group Theory (LV)
Isomorphism of a Group
Automorphism of a Group
Inner Automorphism of a Group
Let G be any group, g a fixed element in G. Define phi:G--> G by phi(x) = gxg^-1.
Prove that phi is an isomorphism of G onto G.
The fully formatted problem is in the attached file.
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