Build a sporadic group in your basement

Paul Becker, Martin Derka, Sheridan Houghten, Jennifer Ulrich

Research output: Contribution to journalArticle

Abstract

All simple finite groups are classified as members of specific families. With one exception, these families are infinite collections of groups sharing similar structures. The exceptional family of sporadic groups contains exactly twenty-six members. The five Mathieu groups are the most accessible of these sporadic cases. In this article, we explore connections between Mathieu groups and error-correcting communication codes. These connections permit simple, visual representations of the three largest Mathieu groups: M24, M23, and M22. Along the way, we provide a brief, nontechnical introduction to the field of coding theory.

Original languageEnglish (US)
Pages (from-to)291-305
Number of pages15
JournalAmerican Mathematical Monthly
Volume124
Issue number4
DOIs
StatePublished - Apr 1 2017

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Sporadic Groups
Finite Simple Group
Coding Theory
Exception
Sharing
Family

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Becker, Paul ; Derka, Martin ; Houghten, Sheridan ; Ulrich, Jennifer. / Build a sporadic group in your basement. In: American Mathematical Monthly. 2017 ; Vol. 124, No. 4. pp. 291-305.
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Build a sporadic group in your basement. / Becker, Paul; Derka, Martin; Houghten, Sheridan; Ulrich, Jennifer.

In: American Mathematical Monthly, Vol. 124, No. 4, 01.04.2017, p. 291-305.

Research output: Contribution to journalArticle

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