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November 24th, 2010, 04:21 AM   #1
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Question about def. of additive groups

Hi!

Just a little question about the def. of additive groups. It just mean a group whose binary operation we do not know, but
it is closed under addition righ? It does not mean that the groups binary operation necessarily is addition...
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November 24th, 2010, 04:56 AM   #2
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Re: Question about def. of additive groups

It means a *group* whose operation we call "addition". So not only is it closed under the operation, but it is associative under the operation and there is an inverse for that operation.
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November 24th, 2010, 05:49 AM   #3
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Re: Question about def. of additive groups

Also, the notation is a bit different.
Rather than writing
a ? (a^-1) = e
(where e is the identity element), you can write
a + (-a) = 0
since the additive inverse of an element is its opposite/negative.
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November 24th, 2010, 05:55 AM   #4
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Re: Question about def. of additive groups

It tends to be contextual as to whether a group is written additively or multiplicatively. By convention, groups are almost never written additively if they are not Abelian (commutative with respect to the operation). Strictly speaking however, the only difference is one of notation, as noted above.
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November 24th, 2010, 06:57 AM   #5
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Re: Question about def. of additive groups

mhm, ok I see. Thanks for all the feedback.
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