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Question about def. of additive groupsHi! 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... |

Re: Question about def. of additive groupsIt 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. |

Re: Question about def. of additive groupsAlso, 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. |

Re: Question about def. of additive groupsIt 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. |

Re: Question about def. of additive groupsmhm, ok I see. Thanks for all the feedback. |

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