Talk:Abstract Algebra/Group Theory/Subgroup

It seems to me that theorem 5 is only true if the group, G, is finite. For an infinite group (say, the integers), it is clearly not possible to generate the identity element from an arbitrary element and so anything generated from an element other than the identity cannot be a subgroup. Furthermore, the identity element can only generate the trivial group (since e * e = e). Should the statement of the theorem should be modified to specify that G must be a finite group? 128.29.43.2 (discuss) 20:22, 15 July 2013 (UTC)

G is generated from a generator with the binary operation applied an integer number of times (not a natural number of times)--this allows the identity to be generated and the formation of an infinite cyclic group.128.29.43.3 (discuss) 15:07, 17 July 2013 (UTC)