IB Maths HL Option Sets Isomorphism

Operation table of a group, Symmetries of plane figures, Cycle notation for permutations, Left and right cosets, group homomorphism, kernel, kernel and range of a homomorphism, isomorphisms

IB Maths HL Option Sets Isomorphism

Postby elizabeth » Thu Mar 07, 2013 7:47 pm

IB Mathematics HL Option: Sets, Relations and groups (Groups-Isomorphism)


How can we show that the function defined by is an isomorphism between and

Thanks
elizabeth
 
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Re: IB Maths HL Option Sets Isomorphism

Postby miranda » Thu Mar 07, 2013 8:13 pm

IB Mathematics HL Option: Sets, Relations and groups (Groups-Isomorphism)

The definition of isomorphism is
Two groups {G,*} and {H,o} are isomorphic if:
- there is a bijection
and for every


and for your question we have
is a group under addition
and is a group under multiplication, and is a bijection from into


defined by is an

isomorphism between and

Since f has inverse function and we have the following



Hope these help :) :) :)
miranda
 
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