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1. Prove that if G=, then G=

2007-10-23 13:40:14 · 1 answers · asked by Anonymous in Science & Mathematics Mathematics

1 answers

You probably mean cyclic GROUP.

I answered this for somebody in another thread recently. But come to think of it, I can see a cleaner proof.


A. x^(-1) is contained in G. That's part of the definition of subgroup.
B. But then it's immediately obvious that the group generated by x^(-1) is contained in G.
C. Let y = x^(-1). Then obviously y^(-1)=x. From that, the result in B can be immediately applied to also show G is contained in
D. B and C, taken together, immediately prove the desired result.

2007-10-23 20:14:52 · answer #1 · answered by Curt Monash 7 · 0 0

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