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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

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

Thanks

- elizabeth
**Posts:**0**Joined:**Mon Jan 28, 2013 8:09 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

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
**Posts:**268**Joined:**Mon Jan 28, 2013 8:03 pm

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