Prove that group has no finite set of generators.

Any help would be appreciated!

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- Feb 20th 2011, 07:02 AMdougGroup theory
Prove that group has no finite set of generators.

Any help would be appreciated! - Feb 20th 2011, 07:24 AMroninpro
For the ease of notation, suppose there are two generators, . Let be a prime such that . Is it possible to write as a combination of ?

You can generalize this argument for any supposed number of generators.