First isomorphism theorem

  • #1

Homework Statement



can someone explain the 1st isomorphism theorem to me(in simple words) i really dont get it

Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
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Why don't you write down the 1st isomorphism theorem, so people here will actually know what are you talking about. Not everybody might have learned that theorem adressed with the same name as you!
 
  • #3
If G and H are groups and f is a homomorphism from G to H, then the kernel K of f is a normal subgroup of G, the image of f is a subgroup of H, and the quotient group G /K is isomorphic to the image of f.
 
  • #4
HallsofIvy
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If f: G-> H, then

The kernel, K, of f is a subgroup of G - {x in G such that f(G)= eH}

The Image, I, of f is a subgroup of H- {y in H such that y= f(x) for some x in G}

1) K is a normal subgroup of G.

2) G/K is isomorphic to I.

Do you understand what "homomorphism" and "isomorphism" mean? Do you understand what a "normal subgroup" is and what "G/K" is?
 
  • #5
can you specify G/K is isomorphic to I.
 

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