Davenport constant and its variants for some non-abelian groups

We define two variants e (G), f (G) of the Davenport constant d (G) of a finite group G, that is not necessarily abelian. These naturally arising constants aid in computing d (G) and are of potential independent interest. We compute the constants d (G), e (G), f (G) for some nonabelian groups G, and demonstrate that, unlike abelian groups where these constants are identical, they can each be distinct. As a byproduct of our results, we also obtain some cases of a conjecture of J. Bass. We compute the k-th Davenport constant for several classes of groups as well. We also make a conjecture on f (G) for metacyclic groups and provide evidence towards it.