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Cayley's theorem

   Also found in: Wikipedia 0.01 sec.
Cayley's theorem [′kā‚lēz ‚thir·əm]
(mathematics)
A theorem that any groupGis isomorphic to a subgroup of the group of permutations onG.
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This representation was first used in the proof of Cayley's theorem [4] to show a one-to-one correspondence between free labeled trees on n nodes and strings of length n-2.
An optimal algorithm for Prufer codes by Wang, Xiaodong; Wang, Lei; Wu, Yingjie / Journal of Software Engineering and Applications (JSEA)
He takes a modern, geometric approach to group theory, which is particularly useful in the study of infinite groups, focusing on Cayley's theorems first, including his basic theorem, the symmetry groups of graphs, or bits and stabilizers, generating sets and Cayley graphs, fundamental domains and generating sets, and words and paths.
Groups, graphs, and trees; an introduction to the geometry of ... by SciTech Book News
For example, before the proof of Cayley's theorem (2) is introduced, students are asked to suggest possible correspondences between words and trees.
Reducing abstraction when learning Graph Theory by Hadar, Irit / Journal of Computers in Mathematics and Science Teaching
 
 
 
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