a) List all the cyclic subgroups of <Z10, +> (Z10 = integers mod 10)

b) Show that Z10 is generated by 2 and 5

c) Show that Z2 x Z3 is a cyclic group

Any help is appreciated.... Thanks.

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- October 8th 2010, 11:42 PMjzelltGenerators of Groups
a) List all the cyclic subgroups of <Z10, +> (Z10 = integers mod 10)

b) Show that Z10 is generated by 2 and 5

c) Show that Z2 x Z3 is a cyclic group

Any help is appreciated.... Thanks. - October 9th 2010, 03:47 AMSwlabr
Take every element and work out the subgroup generated by them. For example, as .

. That is to say, it is generated by the element 1. So, if you can prove that then you are done. You can prove that by noting that 2 and 5 are coprime, so...

You want to find a single element which generates this group. So, try a few...