What Is the Order of the Intersection of Two Subgroups with Orders 12 and 5?

[karush]

Suppose H and K are subgroups of a group G. If $|H|=12$ and $|K|=5$, and $|H/K|$. Generalize.
$\vert H \cap K\vert=1$
then find $|H ∩ K|.Abstract Algebra
$H ∩ K ≤ H and H ∩ K ≤ K \implies |H ∩ K|||H| and |H ∩ %K|||K| \implies |H ∩ K||12 and |H ∩ K||35
\implies |H ∩ K|| gcd(12, 35)
\implies |H ∩ K|$

ok hopefully this is basically correct but what is the markup code for implies

https://dl.orangedox.com/XIYqaX59YzCfCQoBcb

 

[jvicens]

Hello! Yes, your reasoning is correct. The markup code for implies is \implies, which is used to indicate logical implication in mathematical expressions. So the statement "A \implies B" would mean "If A is true, then B is also true." In this case, we can write "|H ∩ K| \implies gcd(12, 35)" to indicate that the order of the intersection of H and K implies the greatest common divisor of the orders of H and K. I hope this helps!