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设(H，)是群(G，)的子群，如果A={x|x∈G，xHx^-1=H}，证明：(A，)是(G，)的子群．

【参考答案】

任取x，y∈A，有x，y∈G，且x*H*x^-1=H，y*H*y^-1=H．因为......

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设G={[1]，[2]，[3]，[4]，[5]，[6]}，G上的二元运算×7如表5-36所示．(G，×7)是循环群吗?若是，请找出它的生成元．表5-36 ×7 [1] [2] [3] [4] [5] [6] [1] [1] [2] [3] [4] [5] [6] [2] [2] [4] [6] [1] [3] [5] [3] [3] [6] [2] [5] [1] [4] [4] [4] [1] [5] [2] [6] [3] [5] [5] [3] [1] [6] [4] [2] [6] [6] [5] [4] [3] [2] [1]

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