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Communicated by M. F. Newman ABSTRACT. Many one-relator groups with center have been shown to be of the form -A necessary and a sufficient condition for the sequence (Pi,Qi,P 2 >Q2> '",Pt>Qt) a r e given in order for groups of the above form to be one-relator groups.

A coin set is a strictly increasing list of positive integers that always begins with 1. A coin set is called greedy when the simple greedy change-making algorithm always produces the fewest number of coins in change. Here, the greedy change-making algorithm repeatedly selects the largest denomination coin less than the remaining amount until it has assembled the correct change. Pearson has provided an efficient algorithm for determining whether a coin set is greedy. We study a stricter property on coin sets, called total greediness, which requires that all initial subsequences of the coin set also be greedy, and a simple property makes it easy to test if a coin set is totally greedy. We begin to explore the theory of greedy obstructions– those coin sets that cannot be extended to greedy coin sets by the addition of coins in larger denominations.

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