Cantor Groups

by Ben Mathes, Chris Dow, and Leo Livshits

College Mathematics Journal
January, 2011

Subject classification(s): Analysis | Real Analysis
Applicable Course(s): 4.2 Mod Algebra I & II | 4.11 Advanced Calc I, II, & Real Analysis

The Cantor subset of the unit interval $[0,1)$ is large in cardinality and also large algebraically, that is, the smallest subgroup of $[0,1)$ generated by the Cantor set (using addition mod $1$ as the group operation) is the whole of $[0,1)$. The authors show how to construct Cantor-like sets which are large in cardinality but small algebraically.

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