I have recently been looking at Hall's marriage theorem. One application of it is that given a finite group $G$ and a subgroup $H\leq G$, there is a left transversal of $H$ that is also a right transversal. I can see the theoretical importance of this, but am struggling to find any situations when one would actually use this. If anybody can enlighten me, that would be greatly appreciated.
Left and right transversals of groups.
8
$\begingroup$
group-theory
finite-groups
-
0Do you mean a left traversal of $H$? http://mathworld.wolfram.com/LeftTransversal.html – 2012-04-20
-
0@ThomasAndrews Yes, I do mean a left transversal of $H$. Thanks for pointing out the (now corrected) error. – 2012-04-20