TY - JOUR
T1 - Build a sporadic group in your basement
AU - Becker, Paul E.
AU - Derka, Martin
AU - Houghten, Sheridan
AU - Ulrich, Jennifer
N1 - Publisher Copyright:
© The Mathematical Association of America.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - 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.
AB - 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.
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U2 - 10.4169/amer.math.monthly.124.4.291
DO - 10.4169/amer.math.monthly.124.4.291
M3 - Article
AN - SCOPUS:85020756367
SN - 0002-9890
VL - 124
SP - 291
EP - 305
JO - American Mathematical Monthly
JF - American Mathematical Monthly
IS - 4
ER -