[代數] subgroup判別 (integers with addition)
Q: Let p, q: distinct primes.
J=proper subgroup of the additive group of integers which
contains exactly 3 elements of the set {p, p+q, pq,p^q, q^p}
Which 3 elements are in J?
(A) pq, p^q, q^p
(B) p, pq, p^q
(C) p, p^q, q^p
(D) p, p+q, pq
Ans: B
詳解寫說: any additive group of integers Z is in the form c*Z, c is in Z
剛開始做這題的時候 覺得那五個elements不可能取三個還能closed in addition,
除非有個q, 覺得這題impossible.... 但是他還真的有解不是typo....
只是看了解還是疑惑 有人能幫忙解答嗎？謝謝`
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