1. ## cyclic group

Show that < Z(mod2) X Z(mod3), +> is a cyclic group. The Z's have 2 and 3 has subscripts...

2. Originally Posted by nikie1o2
Show that < Z(mod2) X Z(mod3), +> is a cyclic group. The Z's have 2 and 3 has subscripts...

Hint - Lemma: if $x,y$ are two elements of finite coprime order in a group and they commute (i.e., $xy=yx$), then $ord(xy)=ord(x)ord(y)$

Tonio