Hello everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I was wondering if the following claim is true:

Let ##G_1## and ##G_2## be finite cyclic groups with generators ##g_1## and ##g_2##, respectively. The group formed by the direct product ##G_1 \times G_2## is cyclic and its generator is ##(g_1,g_2)##.

I am not certain that it is true. If I make the following stipulation

Let ##G_1## and ##G_2## be finite cyclic groups with generators ##g_1## and ##g_2##, respectively,and thegroup formed by the direct product##G_1 \times G_2##is cyclic,then it has the generator ##(g_1,g_2)##.

this might be true. However, I would like to hear from you before I try to go prove something that is false.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Direct Product of Cyclic Groups

**Physics Forums | Science Articles, Homework Help, Discussion**