American Mathematical Monthly, volume 107, number 7, by The Mathematical Association of America

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Does the field have a core? The parochialism of mathematicians may be unwise, but it is explained and in part justified by the long history and continuing triumphs of a deep discipline. Mathematicians, and even some others, understand that this inward-looking field produces both profound beauty and "unreasonably effective" tools for other sciences. Statistics, in contrast, coalesced in this century from beginnings in many fields and may be about to dissipate back into many fields. It isn't clear what "statisticians" engaged in market research and molecular biology have in common.

In many cases, deans contrasted mathematics with statistics, which they pointed out had connections everywhere. In suggesting that mathematics has become insular and statistics imperiled, we invite debate, but we attempt to argue from data and hope others will do likewise. rs 2. STATISTICS DIFFERENT. We begin by outlining the ways in which statistics is the healthier discipline. Among the encouraging vital signs, we find increasing enrollment and a consensus on teaching, more non-academic employment and links to many academic fields, and a positive response to technological change.

We define abelian and nilpotent numbers analogously. Recall that a group is nilpotent if and only if it is the (internal) direct product of its Sylow subgroups; see [7, 126]. This is not a new problem; the cyclic case is attributed to Burnside and has appeared in numerous articles, [9], [4], [1], [2]. The abelian case appears as a problem in an old edition of Robinson's book in group theory; see also [6] and the nilpotent case was also done quite some time ago (see [5], [6]). In this article we give an arithmetic characterization of the cyclic, abelian, and nilpotent numbers from a single perspective.

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