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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]

A.(G，×₇)是循环群吗?若是，请找出它的生成元．

【参考答案】

显然，(G，×₇)是封闭的，具有结合律．[1]为它的单位元，[2]与[4]、[3]与[5]互为逆元......

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