if $G$ is a EDP of two finite groups A and B. then order of element $(a,b)\in G=A\times B$ is lcm of order of a and order of b.

Question

If $G$ is a external direct product of two finite groups $A$ and $B$, then order of element $(a,b)\in G=A\times B$ is lcm of order of $a$ and order of $b$.

So it is. Did you have any question you wanted to ask? – hmakholm left over Monica Sep 14 '13 at 16:29 — hmakholm left over Monica, Sep 14 '13 at 16:29

score 1 · Answer 1 · answered Sep 14 '13 at 16:28

1

Consider when is it that $(a, b)^{n} = (a^{n}, b^{n}) = (1, 1)$.

answered Sep 14 '13 at 16:28

Andreas Caranti

68,873

if $G$ is a EDP of two finite groups A and B. then order of element $(a,b)\in G=A\times B$ is lcm of order of a and order of b.

1 Answers1