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Finitely Generated Abelian Groups
1988A group is finitely generated if it has a finite set of generators. Finitely generated abelian groups may be classified. By this we mean we can draw up a list (albeit infinite) of “standard” examples, no two of which are isomorphic, so that if we are presented with an arbitrary finitely generated abelian group, it is isomorphic to one on our list.
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Finitely Generated Abelian Groups
1980In order to solve our particular problem of finding all possible abelian groups of order p2, p prime, or even the larger problem of finding all possible abelian groups of given order n, we need to consider the structure of finite abelian groups only. However, it turns out to be not much more difficult to find the structure of a wider class of abelian ...
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Finitely Generated Abelian n-Ary Groups
Journal of Mathematical SciencesThe structure of finitely generated abelian groups is well-known. In this paper, the author provides a similar result for finitely generated \(n\)-ary abelian groups. An \(n\)-ary group \((G, f)\) is called abelian if and only if for all \(x_1, x_2, \ldots, x_n\in G\) and all permutation \(\sigma\), we have \[ f(x_{\sigma(1)}, x_{\sigma(2)}, \ldots, x_{
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Cancer statistics for adolescents and young adults, 2020
Ca-A Cancer Journal for Clinicians, 2020Kimberly D Miller +2 more
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Obesity and economic environments
Ca-A Cancer Journal for Clinicians, 2014Roland Sturm, Ruopeng An
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Who's still smoking? Disparities in adult cigarette smoking prevalence in the United States
Ca-A Cancer Journal for Clinicians, 2018Alex C Liber +2 more
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