We study randomized test-and-set (TAS) implementations from registers in the asynchronous shared memory model with n processes. We introduce the problem of group election, a natural variant of leader election, and propose a framework for the implementation of TAS objects from group election objects. We then present two group election algorithms, each yielding an efficient TAS implementation. The first implementation has expected max-step complexity O(log* k) in the location-oblivious adversary model, and the second has expected max-step complexity O(log log k) against any read/write-oblivious adversary, where k ≤ n is the contention. These algorithms improve the previous upper bound by Alistarh and Aspnes [2] of O(log log n) expected max-step complexity in the oblivious adversary model. We also propose a modification to a TAS algorithm by Alistarh, Attiya, Gilbert, Giurgiu, and Guerraoui [5] for the strong adaptive adversary, which improves its space complexity from super-linear to linear, while maintaining its O(log n) expected max-step complexity. We then describe how this algorithm can be combined with any randomized TAS algorithm that has expected max-step complexity T(n) in a weaker adversary model, so that the resulting algorithm has O(log n) expected maxstep complexity against any strong adaptive adversary and O(T(n)) in the weaker adversary model. Finally, we prove that for any randomized 2-process TAS algorithm, there exists a schedule determined by an oblivious adversary such that with probability at least 1/4t one of the processes needs at least t steps to finish its TAS operation. This complements a lower bound by Attiya and Censor-Hillel [7] on a similar problem for n ≥ 3 processes.