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Prove that if (H,o) and (K,o) are subgroups of a group (G,o), then (H [tex]\cap[/tex] K,o) is a subgroup of (G,o).
Proof:
The identity e of G is in H and K, so e [tex]\in[/tex] H[tex]\cap[/tex]K and H[tex]\cap[/tex]K is not empty. Assume j,k [tex]\in[/tex] H[tex]\cap[/tex]K. Thus jk[tex]^{-1}[/tex] is in H and K, since j and k are in H and K. Therefore, jk[tex]^{-1}[/tex] [tex]\in[/tex] H [tex]\cap[/tex] K making H[tex]\cap[/tex]K a subgroup.
Just trying to check this proof and see if I did a a good job at it.
Let (G,o) be an Abelian group and let a,b [tex]\in[/tex] G, Prove that (a o b)[tex]^{2}[/tex]=a[tex]^{2}[/tex] o b[tex]^{2}[/tex]
Not sure where to begin with this proof. Any help?
Proof:
The identity e of G is in H and K, so e [tex]\in[/tex] H[tex]\cap[/tex]K and H[tex]\cap[/tex]K is not empty. Assume j,k [tex]\in[/tex] H[tex]\cap[/tex]K. Thus jk[tex]^{-1}[/tex] is in H and K, since j and k are in H and K. Therefore, jk[tex]^{-1}[/tex] [tex]\in[/tex] H [tex]\cap[/tex] K making H[tex]\cap[/tex]K a subgroup.
Just trying to check this proof and see if I did a a good job at it.
Let (G,o) be an Abelian group and let a,b [tex]\in[/tex] G, Prove that (a o b)[tex]^{2}[/tex]=a[tex]^{2}[/tex] o b[tex]^{2}[/tex]
Not sure where to begin with this proof. Any help?