[代數] 子群的定義
想請問一下以下的敘述為什麼有瑕疵 ?
44. Find the flaw in the following argument: "Condition 2 of Theorem 5.14
is redundant, since it can be derived from 1 and 3, for let a \in H.
Then a^{-1} \in H by 3, and by 1, aa^{-1} = e is an element of H,
proving 2."
(Theorem 5.14: A subset H of a group G is a subgroup of G if and only if
1. H is closed under the binary operation of G,
2. the identity element e of G is in H,
3. for all a \in H it is true that a^{-1} in H also. )
這本書中子群的定義是 G 的子集 H 必須要是一個群, 且 H 上的二元運算 * 必須是
G 的二元運算 * 的 induced operation.
謝謝!
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