[代數] order of a group
需要幫忙確認做法正確~~ Thanks :)
If the finite group G contains a subgroup of order 7
but no element (other than the identity) is its own inverse,
then the order of G could be
A.27 B.28 C.35 D.37 E.42
By Larange, A,D 刪掉
no element (other than the identity) is its own inverse
這句話其實有點不懂
意思是 a =! a' for all a belongs to S\{identity} 嗎？
ps.這邊我讓S表示subgroup of G. a'表示inverse of a
如果意思是這樣，從這個條件可以得知G has no subgroup of order 2
(因為如果a = a', 那aa=aa'=identity, subgroup of order 2)
然後B,E就被刪掉
答案剩下C
ps. 其實關於order of an element & order of a group我有點困惑
order of a group 是指cardinality
order of an element 是指最小的m, st a^m=identity.
但有時候order of an element的定義似乎又可以用來定義order of a group
是不是我弄混了什麼事呢？
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