Cantor Groups

by Ben Mathes, Chris Dow, and Leo Livshits

This article originally appeared in:
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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