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#### GreenGoblin

##### Member

- Feb 22, 2012

- 68

Gracias,

GreenGoblin

- Thread starter GreenGoblin
- Start date

- Thread starter
- #1

- Feb 22, 2012

- 68

Gracias,

GreenGoblin

- Jan 30, 2012

- 2,502

For a start, see this page from The Math Forum.

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- #3

- Feb 22, 2012

- 68

- Jan 30, 2012

- 2,502

I am not sure what "the group of $g^{2}$" means. Could you post your proof?

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- #6

- Feb 22, 2012

- 68

I just showed algebraically gh = hg, without using the fact $(gh)^{2}=1$.

- Feb 15, 2012

- 1,967

it is not the case that all groups are abelian, only some groups are.

a typical proof starts out like this:

suppose $g^2 = 1$ for all g in G. let g, h be any two elements of G (which perhaps might be the same element, if |G| = 1).

then gh is an element of G, so

$(gh)^2 = 1$, that is:

ghgh = 1. then,

g(ghgh) = g(1) = g, and...?