Math Is Fun Forum

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Check

   

I stop here because I don't know how to show the inverse must be in the intersection of H1 and H2.

And anoher question , show that the union of H1 and H2 is not a group , I think I need to use contradiction right?

Last edited by Stanley_Marsh (2007-05-14 09:26:03)

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Numbers are the essence of the Universe

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Check

You have shown that the intersection of two subgroups is closed under the group operation. I don’t see why the same method can’t be used to show that the inverses also belong to the intersection.

The union is two subgroups is not a subgroup. For example, the even integers and the set of all multiples of 3 are subgroups of the additive group of the integers, but their union is not. I’ll let you show that it’s not a subgroup.

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: Check

I worked out the proof

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Numbers are the essence of the Universe

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Check

You are actually proving this statement:

However there is a vital step missing in your proof. Assuming to the contrary that the union was a group, you showed that

Last edited by JaneFairfax (2007-05-15 05:17:37)

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: Check

Yea , I got it .  b=a^-1 (ab) , when couldnt I think of that.

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Numbers are the essence of the Universe