我再试试看。


Let a,b in {g1,g2,...gn}. Since cosets partitions G, we have a!=b iff aH!=bH, and a!=b iff Ha!=Hb. Hence Ha!=Hb iff aH!=bH ... (1)


Suppose there exists g in G and h in H such that ghg^-1 not in H. Observe ghH=gH, hence according to (1), Hgh=Hg, but then Hghg^-1=H, i.e., ghg^-1 in H. Contradiction.





【 在 gtgtjing 的大作中提到: 】
: 我又没要求左陪集等于右陪集
【 在 philbloo 的大作中提到: 】
: 题目的条件就是 H 的 left cose...
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