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Feb 1, 2015 at 14:04 comment added YCor @Pablo "$k$-generated" means generated by some $k$-tuple of elements. Hence 3-generated implies 2-generated by definition, and the trivial group is 17-generated. The optimal number is encapsulated in the (generating) rank, which is by definition the least $k$ such that $G$ is $k$-generated.
Feb 1, 2015 at 13:05 comment added Andrei Jaikin @Pablo I have edited the answer.
Feb 1, 2015 at 13:04 history edited Andrei Jaikin CC BY-SA 3.0
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Feb 1, 2015 at 12:07 vote accept Pablo
Feb 1, 2015 at 12:02 comment added Pablo Andrei, is $T$ free pro-$q$ and not free pro-$p$? Also, $T$ is $2$-generated and not $3$-generated.
Feb 1, 2015 at 10:19 history answered Andrei Jaikin CC BY-SA 3.0