- #1
Bashyboy
- 1,421
- 5
Hello everyone,
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 the group 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.
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 the group 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.