An infinite group with itself as the inverse?
An infinite group with itself as the inverse?
Is it possible to prove or disprove the existent of such an infinite group (G,*), that for any element a belongs to G, a*a = e?

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 Joined: Sun Apr 04, 2010 1:08 pm
Re: An infinite group with itself as the inverse?
Consider the infinite binary sequences. In other words, an element of G is something like (0, 0, 1, 0, 1,1, ...)
The group addition would be adding component wise. In this case, the 0 sequence would be the identity, and every element has order 2.
You can also think of this as (Z/2Z)^N
where Z is the integers and N is the naturals
The group addition would be adding component wise. In this case, the 0 sequence would be the identity, and every element has order 2.
You can also think of this as (Z/2Z)^N
where Z is the integers and N is the naturals
Re: An infinite group with itself as the inverse?
wow. that's a really good example. thank you very much.blitzer6266 wrote:Consider the infinite binary sequences. In other words, an element of G is something like (0, 0, 1, 0, 1,1, ...)
The group addition would be adding component wise. In this case, the 0 sequence would be the identity, and every element has order 2.
You can also think of this as (Z/2Z)^N
where Z is the integers and N is the naturals