Is the following statement is true or False ?
let G be a finite group with a normal subgroup H such that $\frac{G}{H}$ has order $7$. then $G\cong H \times \frac {G}{H}$
im thinking that the statement will be true because if i take $G= Z_{14}$ and$ H= Z_7$ now $ Z_{14} =Z_7 \times Z_2$
which is satisfied the above statement . so from my point of view this statment is true ..
Is its corrects ?...........
Hint: When is $\Bbb Z_{mn}$ not isomorphic to $\Bbb Z_m\times \Bbb Z_n$?