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#1 2007-05-14 09:24:41

Stanley_Marsh
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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)


Numbers are the essence of the Universe

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#2 2007-05-14 11:10:55

JaneFairfax
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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. smile

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#3 2007-05-14 17:54:48

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: Check

I worked out the proof


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#4 2007-05-15 00:03:40

JaneFairfax
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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)

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#5 2007-05-15 04:50:13

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.


Numbers are the essence of the Universe

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